Grade 8 MATH Term 2 Week 5: Linear Equation in One Variable | MATATAG - 2nd Term/3rd Quarter Tagalog — Transcript

Full transcript

1. 0:07[bell]
2. 0:09Hello everyone, welcome Matt ACP YouTube
3. 0:12channel where you can find free Tagalog
4. 0:13mathematics tutorial. Our topic for
5. 0:16today is all about linear equation in
6. 0:18one variable. But before we begin, let
7. 0:20me just remind everyone to please click
8. 0:22the subscribe buttons.
9. 0:26And to those who have already
10. 0:27subscribed, thank you very much for
11. 0:29sharing also our videos to others,
12. 0:31especially to our dear teachers. Thank
13. 0:33you for sharing this to our dear
14. 0:35learners. So without further ado, let's
15. 0:37now begin with our lesson. All right,
16. 0:39our competency for today is to solve
17. 0:42linear equations in one variable. All
18. 0:44right, so let's begin with a recall. So
19. 0:47remember we already learned about
20. 0:48algebraic expressions in grade 7. So
21. 0:51remember algebraic expression is a
22. 0:53combination of variables, constants and
23. 0:56operations. So we have here the
24. 0:58examples. We have x + 3 where we have
25. 1:00the variables x and you constant three.
26. 1:03We also have here x - y where we have
27. 1:06variables only and the operation
28. 1:08subtraction. Me xy which means x * y. So
29. 1:13it is still an algebraic expression. 2x
30. 1:17+ y wherein we have now multiplication
31. 1:20and addition meaning 2 * x and then plus
32. 1:23y. We also have here x over y which
33. 1:25means x / y and then we have here
34. 1:29exponents. We have a 2 + b ^ 2 meaning a
35. 1:32* a and then b * b. Okay, so if we're
36. 1:36going to add it, it will be a 2 + b ^ 2.
37. 1:39And we also have here expressions like 1
38. 1:42+ 3 and then we have 4 + -6. Well, these
39. 1:45are just what we call numerical
40. 1:47expressions. But are they algebraic
41. 1:48expressions?
42. 1:50Algebraic expressions, it should have
43. 1:52variables, constants, and operations.
44. 1:55Okay, let's have equation.
45. 1:59Equation. Okay, remember equation is a
46. 2:01mathematical statement that shows the
47. 2:03two expressions are equal. Okay, that's
48. 2:06why we have the word equation coming
49. 2:08from the root word equal. So just like
50. 2:11in a balance scale wherein one side will
51. 2:15be equal to another side if they have
52. 2:17the same weight. Just like for example
53. 2:18here equal
54. 2:21we have here x + 3 and then we have here
55. 2:23five value left side
56. 2:27right side. Okay
57. 2:29equation. Well here we have an unknown
58. 2:32value which is x. Remember variable is
59. 2:35unknown. We do not know the value. that
60. 2:37whatever the value is
61. 2:39value x it will make the statement true
62. 2:43still equation. Okay. So whatever the
63. 2:48value of x here it will make the
64. 2:50statement equal. So
65. 2:53value x
66. 2:55solving equation that we also have
67. 2:57learned before. So when we solve
68. 2:59equation it means finding the value of
69. 3:02the unknown that makes the equation
70. 3:03true. Canina we have here x + 3 is equal
71. 3:06to 5. How are we going to get the value
72. 3:09of x? Well x here is something that will
73. 3:13make the statement true. So what will
74. 3:15you add to three para five? So it will
75. 3:18be positive2. Okay. Therefore we have
76. 3:21now 2 + 3 is 5. So 5 is equal to 5. The
77. 3:24statement is now true.
78. 3:29Solution
79. 3:31solution equation. All right. Now let's
80. 3:34have the properties of equality because
81. 3:36this is also very important. Okay
82. 3:39equation.
83. 3:42So remember we have the first one we
84. 3:44have the reflexive property of equality
85. 3:46which states that a is equal to a. Just
86. 3:50like in a mirror if you face the mirror
87. 3:53you will see your own reflection. Okay.
88. 3:56Reflexive property of equality. Okay.
89. 3:59Next one we also have here symmetric
90. 4:01property of equality which states that
91. 4:03if a is equal to b then b is now equal
92. 4:06to a. Okay it's just like a uh
93. 4:10symmetrical figure like for example here
94. 4:13the left side is symmetrical to the
95. 4:15right side of a butterfly. So if a is
96. 4:18equal to bal
97. 4:20b is equal to a. Next we also have here
98. 4:22transitive property of equality. If A is
99. 4:25equal to B and B is equal to C, then A
100. 4:28is equal to C. Okay.
101. 4:32Example, we have here three boys with
102. 4:34their height. If boy A and boy B has the
103. 4:37same height, if they have the same
104. 4:38height and B have the same height with
105. 4:40C, boy C, and boy A and boy C also have
106. 4:44the same height. Okay, that is the
107. 4:46meaning of transitive property of
108. 4:48equality. Another property is uh the
109. 4:52addition and subtraction property of
110. 4:54equality. Okay. So here some of the
111. 4:56books they just use addition property of
112. 4:58equality. But uh actually we can use
113. 5:02subtraction property of equality.
114. 5:04Although they are almost the same.
115. 5:08We have here if a is equal to b then a +
116. 5:10c is equal to b plus c. Whatever we add
117. 5:13on the left side of the equation
118. 5:18right side. Now whatever we subtract on
119. 5:20the left side of the equation just like
120. 5:22this a minus c is subtract right side so
121. 5:26b minus c as well. So addition
122. 5:30c and then subtraction
123. 5:33c or any value. All right. Next
124. 5:38illustration.
125. 5:41If we have one person on the left side
126. 5:43and then one person on the right side
127. 5:47person left
128. 5:50right para balance. Okay. What else we
129. 5:53also have here? Multiplication and
130. 5:55division of property of equality wherein
131. 5:58if we have here a plus a is equal to b
132. 6:00I'm sorry then a * c is equal to b * c
133. 6:04whatever we multiply on the left side it
134. 6:07should be also be multiplied on the
135. 6:09right side. and division. If a is
136. 6:13divided by c then b is also divided by
137. 6:16c. Same
138. 6:19okay divide both sides just like here.
139. 6:22Okay.
140. 6:26Left side
141. 6:28right side. Okay. So those are the
142. 6:30properties of equality that we are going
143. 6:32to use in solving uh linear equations.
144. 6:37Okay. So again, if you haven't mastered
145. 6:39these skills, you can actually go back
146. 6:41to our previous videos. This is found in
147. 6:44the grade 7 playlist on algebraic
148. 6:47equations. Like for example, solving
149. 6:48equations using the bar model,
150. 6:50properties of equality, uh solving
151. 6:52equations using properties of equality,
152. 6:54and solving problems involving algebraic
153. 6:56equations. You can always go back to
154. 6:58this if you want to recall or review
155. 7:00your lessons in grade 7.
156. 7:04Okay. So focus linear equation in one
157. 7:07variable. So what is this? A linear
158. 7:09equation in one variable is an equation
159. 7:11that can be written in the form ax plus
160. 7:15b is equal to c. Okay. Wherein a and b
161. 7:19and c are real numbers. Okay. And a
162. 7:22should not be equal to zero. I repeat we
163. 7:24have here a b and c these are all uh
164. 7:28real numbers. And variable is variable
165. 7:32x. is variable. Okay. And one more
166. 7:36thing, a the first coefficient should
167. 7:38not be equal to zero. Okay. Form linear
168. 7:43equation in one variable. Let let us
169. 7:45have examples. Salima, we have here 3x +
170. 7:485 is equal to 11. So is this in the form
171. 7:51a x + b is equal to c? Yes. Because we
172. 7:54have here the variable x and then ano
173. 7:57value a we have here three and then uh
174. 8:00five as our b and then 11 as our c. So
175. 8:04they are all real numbers. 0 first
176. 8:07coefficient. Ano pa. We also have here 7
177. 8:10x - 4 is equal to 10. So the only
178. 8:12variable here is also x. We have the a
179. 8:15which is 7, b which is -4 and then c
180. 8:18which is 10. So not necessarily exactly
181. 8:26consider
182. 8:27examples. No actually we can also have
183. 8:30this example we have here x + 2 is equal
184. 8:33to 6. Oh, so value C is 6 and value B is
185. 8:382. But you might be questioning, you
186. 8:41might be asking A. So here we don't have
187. 8:45a number before X. But we know that if
188. 8:48it is uh not written
189. 8:511
190. 8:53coefficient. So our A is equal to 1. Ano
191. 8:56P. We also have here 5X is equal to -20.
192. 8:59So -20 here is C. No asan po B.
193. 9:06number or constant. Well, we can say
194. 9:08that B is equal to zero.
195. 9:11Okay. And if we're going to add zero
196. 9:13here, it will be the same. Now, what
197. 9:14will be our A? It is five. Okay. And
198. 9:17remember, A should not be equal to zero.
199. 9:20B C 0 except for the first coefficient.
200. 9:25Okay.
201. 9:26Linear equation in one variable and it
202. 9:30can be written in this form. A X + B is
203. 9:32equal to C. Okay. Okay, just some
204. 9:34additional notes. Okay, example hind
205. 9:37linear equation in one variable. So no
206. 9:39variable in a linear equation is raised
207. 9:41to a power greater than one or use as
208. 9:44the denominator of a fraction or inside
209. 9:47a radical. So take note linear
210. 9:51exponent
211. 9:53power.
212. 9:57So examples we have here x^2 + 1 is
213. 10:00equal to 5. This is not a linear
214. 10:02equation. Why? Because the exponent here
215. 10:04or the power the degree is 2 not 1. What
216. 10:08else we have here? X raised to 3 is
217. 10:10equal to 12. Okay. Uh this exponent is
218. 10:14not one. So therefore this is not a
219. 10:16linear equation. We have here 4x= 3.
220. 10:20This is also not a linear equation
221. 10:22because the variable x is in the
222. 10:24denominator.
223. 10:26Okay. uh in the in our linear equation.
224. 10:29Nothing variable I numerator if it is in
225. 10:33a fraction form. Okay. What else? We
226. 10:36also have here the square root of x + 2
227. 10:38is equal to 5. This is not also a linear
228. 10:41equation because the variable x is
229. 10:44inside the radical. Okay.
230. 10:47All right. So there you go. Those are
231. 10:48examples of not linear equations.
232. 10:52Okay. For you to practice, I have here
233. 10:54an exercise. You can pause this video if
234. 10:56you want to answer this on your own.
235. 10:58Determine whether each of the following
236. 10:59equations is a linear equation in one
237. 11:01variable. Write linear if it is and not
238. 11:04linear if it is not. I'll give you time
239. 11:06to do this and then later you can play
240. 11:08this and then I'll give you the correct
241. 11:10answers.
242. 11:24>> [music]
243. 11:34[music]
244. 11:46>> Okay, I hope you are now ready. Let's
245. 11:48now find out the correct answer. Let's
246. 11:50have here number one 2x + 3 is equal to
247. 11:527. This is a linear equation because the
248. 11:55variable has exponent 1. Number two 4x^2
249. 11:58- 3 is equal to 9. This is not a linear
250. 12:00equation because the variable is raised
251. 12:02to two. Next, it's also not a linear
252. 12:05equation because the variable is in the
253. 12:07denominator. Number four, we have here 7
254. 12:10x - 2 = 12. This is linear equation. The
255. 12:13power of the exponent, I mean the power
256. 12:15of x is 1. Number five, we have here 6x
257. 12:18+ 4 is equal to 2x + 16. This is still a
258. 12:22linear equation because the variable to
259. 12:24the first power on both sides par. Next,
260. 12:27we have here number 6. This is not a
261. 12:29linear equation because the variable is
262. 12:31under a radical symbol. Next, 9 - 3x is
263. 12:34equal to 0. This is linear equation
264. 12:37because the exponent of x here is still
265. 12:391. Okay. CI0. Okay. Next, we have here
266. 12:445x cub is equal to 10. This is not a
267. 12:47linear because the exponent is 3. Next
268. 12:49one we have here 2 uh * x + 1 is equal
269. 12:53to 6. This is linear equation. This can
270. 12:55be simplified as 2x + 2 is equal to 6 by
271. 12:58distributing 2 multiply x 2x 2 * 1 2.
272. 13:04And then lastly this is also a linear
273. 13:06equation because although we have here a
274. 13:07fraction per variable denominator. So
275. 13:11the fraction 1/2 here serves as the
276. 13:14numerical coefficient for our variable
277. 13:16x. Okay. So there you go. I hope.
278. 13:22Okay. Now let's proceed to solving
279. 13:23linear equation in one variable. This
280. 13:26time we will do one step and twoep
281. 13:28equations. Okay. Let's have the first
282. 13:30example. We have here x - 6 is equal to
283. 13:3410. Okay. So goal is to find the value
284. 13:36of x. meaning x left side and then the
285. 13:40other side will be the value of x. So
286. 13:42how are we going to do that? Since we
287. 13:44have here -6
288. 13:46is c6
289. 13:51variable x. And how are we going to do
290. 13:53that? We are going to find the additive
291. 13:55inverse of our uh constant -6. Additive
292. 14:00inverse it's the opposite. If it is -6
293. 14:03the additive inverse is pos 6. So we're
294. 14:06going in short we're going to add pos 6.
295. 14:10Why? Because -6 + 6 will be zeroangal
296. 14:16x left side. And remember in our
297. 14:20property we made mention that if we're
298. 14:23going to add something on the left side
299. 14:26right side
300. 14:30therefore okay
301. 14:3316 okay addition property of equality
302. 14:39a okay so we have now here x is equal to
303. 14:4216 okay using the a right if you want to
304. 14:47check You can do this
305. 14:50value original equation which is x - 6
306. 14:54is equal to 10. So since our x is 16, we
307. 14:57just substitute it here in our original
308. 15:00equation. x will now be 16. And if we're
309. 15:02going to subtract six, will it be the
310. 15:04same with the other side? So let's find
311. 15:06out 16 - 6 is 10. Yes, it is equal. 10
312. 15:10is equal to 10. It this is the value of
313. 15:13x that makes the equation true. Yeah, we
314. 15:16can conclude that our answer is correct.
315. 15:19Okay, X is equal to 16.
316. 15:23Okay, let's have another example. We
317. 15:25have here another one-step equation
318. 15:27example. X + 4 is equal to 7. So
319. 15:334T we are going to find out the additive
320. 15:35inverse. Additive inverse positive4 it
321. 15:39is -4 meaning we just subtract it by
322. 15:42itself. All right, subtract. So 4 - 4
323. 15:45will be 0. Okay. Four. So since
324. 15:51right side. So 7 - 4 will be 3. Okay.
325. 15:57Addition property. We can call it the
326. 15:59subtraction property of equality.
327. 16:02However, okay, we can also use the
328. 16:05addition property of equality. Ano? We
329. 16:08can use AP by adding the additive
330. 16:12inverse. Okay. So which is -4
331. 16:15subtract four but this time you add -4.
332. 16:18So 4 + -4 okay it will make you it will
333. 16:23make this zero. Okay so x will be three
334. 16:26because 7 + -4 is positive 3. Okay so
335. 16:30the bottom line here is we can use the
336. 16:32subtraction property of equality or we
337. 16:34can also use the addition property of
338. 16:37equality. either of the two
339. 16:40you can use both. So we have here x + 4
340. 16:44is equal to 7.
341. 16:46I x i3 will it be equal? So 3 + 4 is
342. 16:51equal to 7. So our answer is correct.
343. 16:57Okay. Next we have here another
344. 16:59equation. We have 5x is equal to 20.
345. 17:02Okay. So we have 5x is equal to 20. goal
346. 17:05separate cx left side
347. 17:09five which is the numerical coefficient.
348. 17:11How are we going to remove five here? So
349. 17:14we can use this method. We can just
350. 17:16divide it by five. Okay. 5 / 5.
351. 17:22Okay. 5 / 5 is 1
352. 17:26x. Okay. And then
353. 17:30five left side. So 20 divided by 5 is 4.
354. 17:35You po division property of equality.
355. 17:38Okay. So the answer is x is equal to 4.
356. 17:41Or we can also use the other method
357. 17:43which is using the multiplication
358. 17:46property of equality by its
359. 17:49multiplicative inverse.
360. 17:53Five. Uh when it comes to multiplicative
361. 17:56inverse five denominator is 1
362. 18:00over 5. So
363. 18:07okay
364. 18:12numerator is one denominator is 5. If we
365. 18:15multiply it here on one side we multiply
366. 18:17it also on the other side. Okay. So
367. 18:20therefore 1/5 over I mean 1/5 * 5 over
368. 18:245. 1 * 5 is 5. 5 * 1 denominator 5 I 5 g
369. 18:3020 * 1 is 20 and then we are going to
370. 18:33divide it by 5 later on. So 5x over 5 we
371. 18:37can cancel out five here is x 20 / 5 the
372. 18:42answer will be four soil. So
373. 18:46okay we can use the division property or
374. 18:49the multiplication property of equality
375. 18:52depend preference.
376. 18:54Okay, let's check if the answer is
377. 18:56correct. Since our x here is four, let's
378. 18:59substitute in the original uh equation.
379. 19:01We have here 5x is equal to 20. Gag 4
380. 19:04cx. So 5 * 4 is 20. So 20 is equal to
381. 19:0920. Therefore, our answer is correct.
382. 19:14Okay. Next example. This time two-step
383. 19:16equation. Since we have here 2x + 2 is
384. 19:19equal to 16.
385. 19:21step.
386. 19:23So first how are we going to remove the
387. 19:26constant 2 here
388. 19:29x okay or 2x so is we will be using the
389. 19:34subtraction property of equality 2 - 2
390. 19:37will be zero so subtract
391. 19:41subtract right side okay next one we
392. 19:44will now have the uh multiplication or
393. 19:47division property of equality why
394. 19:50because we now have 2x is equal to 14
395. 19:52cuz 16 - 2 is 14. How are we going to
396. 19:55remove 2? We will divide it by itself.
397. 19:58Okay, so 2 / 2 will be 1. Okay, 1 is x.
398. 20:03So 14 / 2. Whatever we divide on the
399. 20:07left side right side. So 14 / 2 will be
400. 20:127. x is equal to 7. Okay, we can check
401. 20:15the answer by sub uh substituting. So we
402. 20:18have here 2x + 2 is equal to 16 in our
403. 20:20original equation. Since our x is 7,
404. 20:23let's substitute. So 2 7 x 2 2 * 7 will
405. 20:28be 14 + 2 will it be 16? Yes. Okay, our
406. 20:33answer is correct.
407. 20:38Okay, let's now have example number
408. 20:40five. So again another two-step equation
409. 20:43property.
410. 20:45So we have here 1/4 x - 5 is equal to 1.
411. 20:48So
412. 20:501/4 or -5. Okay.
413. 20:54So we can use the addition property of
414. 20:57equality. Okay. So
415. 21:00we are going to add the additive inverse
416. 21:02which is positive 5.
417. 21:06So add left side right side. So 1 + 5.
418. 21:10Now here on the right side will be 6.
419. 21:13Okay. Tangal -5. Now we only have 1/4 x
420. 21:17is equal to 6. We can now remove you
421. 21:19adding uh coefficient which is 1/4. So
422. 21:22how do we do that? We can use the
423. 21:24multiplication property of equality or
424. 21:27we can multiply 1/4 by its
425. 21:30multiplicative inverse or kanyang
426. 21:32reciprocal which is 4 over 1. Or if you
427. 21:35want to make it simpler you can just
428. 21:36multiply it by four
429. 21:40numerator. Okay. And then 4 over 1. It's
430. 21:44the same with four. So 4 * 1/4. We also
431. 21:48have to multiply
432. 21:506 * 4. So now we have 4 * 1 / 4. So it's
433. 21:554 over 4x. Okay. Or 4x over 4. 6 * 4 is
434. 22:0024. So we can cancel out this one. 4 is
435. 22:031. C x. So we have here x is equal to
436. 22:0824. Therefore our answer is x is equal
437. 22:11to 24. Let's check if this is correct.
438. 22:14No. So let us substitute the original
439. 22:17equation. So 1/4 * x which is 24 - 5 is
440. 22:22equal to 1. So 1/4 * 24 is 24 / 4 - 5 is
441. 22:28equal to 1. 24 / 4 is 6 - 5. Is it going
442. 22:33to be equal to 1? Yes. Okay. 1 is equal
443. 22:36to 1. All right. Therefore, our answer
444. 22:3924 is correct.
445. 22:43Okay. Now, this time let's proceed to
446. 22:45the next part of our lesson. Still on
447. 22:47solving linear equation in one variable,
448. 22:49but this time let's have multi-step
449. 22:51equations. E level up examples for grade
450. 22:568 students. So, we have here example
451. 22:58number one. Uh, as you can see, we have
452. 23:00here a longer uh maybe more complicated,
453. 23:02more complex equations. However, as long
454. 23:06as we know the properties
455. 23:09equations
456. 23:13or more and we can use three or more
457. 23:16properties as well. So, we have here the
458. 23:18first one 2x - 8 and then equals 2 * 3x
459. 23:23+ 4. As you can see, we have variables x
460. 23:27here. Although variable x still this is
461. 23:31considered one variable because we only
462. 23:33have here one type of variable which is
463. 23:36x. Okay. So now we have uh to use the
464. 23:40distributive property of equality. Okay.
465. 23:42Wherein distribute by multiplying 2
466. 23:47expression parenthesis. So 2 * x it will
467. 23:51be 2x 2 next is distributed to8. So 2 *
468. 23:57-8 it will be -6.
469. 24:00Ganun dinang side 2 * 3x will be 6x and
470. 24:04then 2 * 4 will be pos8. Okay there you
471. 24:08go distribute
472. 24:10parenthesis. This time we are now going
473. 24:12to use the addition and subtraction
474. 24:15property of equality. Okay by
475. 24:17segregating
476. 24:20variable side and then sides
477. 24:24constant. Okay. Okay. So we have here
478. 24:262x6.
479. 24:31Okay.
480. 24:34Left side.
481. 24:36So we use addition property of equality.
482. 24:39-16 + 16. Okay.
483. 24:45Okay. Next one. We now use uh
484. 24:48subtraction property of equality by
485. 24:50removing 6x
486. 24:53right side. So 6x minus itself 6x
487. 24:580. Okay. Since - 6x right side - 6x
488. 25:04left side. Therefore we can now add
489. 25:06similar uh terms. We have here 2x - 6x.
490. 25:11Okay. It will be -4x.
491. 25:14While here we have here constant 8 plus
492. 25:17constant 16. It will give you 24. Okay.
493. 25:20Now
494. 25:23numerical coefficient beside x. We can
495. 25:26now use the division property of
496. 25:27equality or we can even use the
497. 25:29multiplication property of equality. So
498. 25:32in this demonstration I will just use
499. 25:34the uh division by just dividing it by
500. 25:37itself. So -4 / itself -4 and then
501. 25:4324 / -4 x will now be equal to -6
502. 25:47because positive / negative is negative.
503. 25:50Okay. The final answer is x is equal to
504. 25:53-6. You can actually check this by
505. 25:56substituting
506. 25:58value x original formula and if it is
507. 26:01the same equal
508. 26:03then this is the correct answer.
509. 26:07Okay. Next example we have here 8 is
510. 26:09equal to 2/3x - 2. So if you notice we
511. 26:12have here the variable x on the right
512. 26:14side of the equation. So if you don't
513. 26:17like this, if you don't want to operate
514. 26:18like this, you can actually move
515. 26:21variable x okay or left side. To do
516. 26:25that, we can actually use the symmetric
517. 26:27property of equality
518. 26:30flip or
519. 26:33right side and 2x 2/3 x - 2 left side.
520. 26:39So there you go. We now have here the
521. 26:41new orientation. 2/3 x - 2 is equal to
522. 26:458. Next, what are we going to do next?
523. 26:47We can use the addition property of
524. 26:49equality to remove -21
525. 26:53variable x. Okay? So, we can add two to
526. 26:57make it zero.
527. 27:01So, this will now be
528. 27:04x. Okay.
529. 27:07L canceled out and then and then we have
530. 27:10here 8 + 2.
531. 27:12Now how are we going to get the value of
532. 27:14x only
533. 27:172/3? We can now use the multiplication
534. 27:20property of equality by multiplying the
535. 27:23multiplicative inverse. Okay. So here we
536. 27:26have 2/3 reciprocal is 3 /2.
537. 27:33So
538. 27:35multiply right side. So 3 / 2 * 2 over
539. 27:393.
540. 27:403 * 2 and then 2 * 3 it will be 6 / 6.
541. 27:4510 * 3 is 30 / 2. It will be like this
542. 27:4930 / 2. Okay. We can now uh simplify
543. 27:52this. We can now cancel out 6.
544. 27:57So x will now be 30 / 2 is 15. Okay.
545. 28:02Final answer. So we have here a
546. 28:04multi-step equation.
547. 28:08Okay. We have here example number three.
548. 28:10Uh as you can see we have the numerator
549. 28:12here x + 4 and then here the numerator
550. 28:15is also an expression algebraic
551. 28:18expression which is 3x - 5. So and para
552. 28:22solve variable x.
553. 28:26So first we can use the cross
554. 28:29multiplication method. Okay, wherein we
555. 28:31multiply the numerator to the
556. 28:34denominator and the denominator to the
557. 28:37numerator of the uh second expression.
558. 28:40Okay, so to do that we have here x + 4 *
559. 28:434
560. 28:46and then 2 * 3x - 5
561. 28:49right side. Okay. So again
562. 28:55numerator multiply denominator
563. 28:58expression. So now to simplify this we
564. 29:02need to distribute using the
565. 29:03distributive property of equality. So 4
566. 29:06* x will be 4x. Okay. And then 4 * 4
567. 29:10will be 16. Okay. On the other side we
568. 29:12have 2 * 3x it will be 6 x. And then 2 *
569. 29:16-5 it will be -10. Now here
570. 29:23we will be using the subtraction
571. 29:24property of equality. So we will
572. 29:27subtract 16
573. 29:32- 16.
574. 29:36So 16 - 16 is okay.
575. 29:42Now 6x right side. So in order for us to
576. 29:46remove 6x here and it transfer left side
577. 29:50we also need to subtract. Okay. So 6x -
578. 29:536x 0. So
579. 29:576x. So we have now here 4x - 6x if
580. 30:00you're going to operate this 4 - 6 will
581. 30:03be -2 and then we just copy x. Then here
582. 30:07on the right side -10 - 16 will be -26.
583. 30:11Okay. At this point since we have here a
584. 30:14negative expression -2x okay
585. 30:18answer value x i mean variable x i
586. 30:23negative
587. 30:26we can actually multiply the whole
588. 30:29equation by -1 okay we can do that
589. 30:33but
590. 30:36using the division property of equality
591. 30:39wherein we are going to divide uh both
592. 30:42sides by -2. Okay.
593. 30:451 and then see -26 / -2. It will now be
594. 30:50positive3. So again we can use
595. 30:52multiplication or the division property
596. 30:55of equality. Okay. So our final answer
597. 30:58is x is equal to 13.
598. 31:02Okay. For example number four, this is a
599. 31:04little bit different. We have here the
600. 31:05absolute value of xus 3 is equal to 7.
601. 31:09So absolute value. All right. Absolute
602. 31:14value. This is the distance of a value
603. 31:19or a number from zero. No. So absolute
604. 31:23value because we are just referring to
605. 31:24the distance. And remember absolute
606. 31:27value is always positive. Okay.
607. 31:34So the first case is if absolute value
608. 31:37of a is equal to b then
609. 31:40is a is equal to b okay positive uh I
610. 31:44mean positive absolute value okay so
611. 31:47here let's assume that value of a is
612. 31:51positive okay we have here x - 3
613. 31:54is we are going to use the property of
614. 31:57equality
615. 31:59-3 by just adding itself 1 -3 + 3 so add
616. 32:053 right side so 7 + 3 x will now equal
617. 32:09to 10 using the AP or the addition
618. 32:11property of equality. Another case
619. 32:15however is what if you absolute value a
620. 32:18is negative. Okay.
621. 32:21Okay.
622. 32:23So a is equal to b. So we have here xus
623. 32:263 is equal to -7. All right. So negative
624. 32:32value. So -7. Now in order for you to
625. 32:35remove -3 here you will apply again
626. 32:37addition property of equality. So plus
627. 32:41uh in effect plus s right side. So -7 +
628. 32:453 it will now be -4. Okay. So there are
629. 32:50two possible answers. Okay.
630. 32:56Equation linear equation involving
631. 32:58absolute value.
632. 33:02Okay. For our last example number five,
633. 33:04we have here the absolute value of 3x -
634. 33:074 is equal to 11. So
635. 33:10cases case one, we have a absolute value
636. 33:14of a is equal to b. Meaning
637. 33:18positive. So we have here 3x - 4 is
638. 33:20equal to 11. Okay. And then we are going
639. 33:23to use addition property.
640. 33:28So 11 + 4 it will now be uh it will now
641. 33:31be 15. Okay. And then we have here 3x is
642. 33:34equal to 15. You can use the division
643. 33:36property of equality to divide three by
644. 33:39itself. 1 and then 15 / 3 is 5. So x is
645. 33:45equal to 5. Now the other case is what
646. 33:48if our answer is negative. Okay. So a is
647. 33:51equal to b. This time we have the
648. 33:53equation 3x is equal to -1 + 4. Okay. So
649. 33:58assuming that 11 here is negative4
650. 34:04using addition property of equality. And
651. 34:07then we have -1 + 4 -7.
652. 34:12And then we can now divide 3x by 3. You
653. 34:15can also divide -7 by 3. Therefore x
654. 34:18will now be equal to -7 over 3. Okay.
655. 34:22Fraction
656. 34:24sagot. Okay. So those are the two cases
657. 34:27or two answers for our uh equation
658. 34:30involving absolute value.
659. 34:34Okay. I hope
660. 34:38so that you will understand it more
661. 34:40clearly. This time we have here
662. 34:42exercises for you to practice your
663. 34:44understanding. You can do this on your
664. 34:45own. Okay. And then you can just pause
665. 34:48this video while you are doing it and
666. 34:49then you can just play it later once you
667. 34:51are done. Compare.
668. 34:54Okay. So, God bless.
669. 35:01Okay. I hope you are now done answering.
670. 35:03Let's now show you the correct answer so
671. 35:05you can check if you have it correctly.
672. 35:08Okay. So, let's have the answers.
673. 35:12Okay. And if ever you can just go back
674. 35:15to our previous examples.
675. 35:19Okay. So, there you go. I hope
676. 35:23discussions our examples a while ago. If
677. 35:25you want more practice, you can actually
678. 35:27answer this uh activity. Okay, you can
679. 35:30do this. You can do this on your own and
680. 35:32then you can just check with your
681. 35:34teachers the answers for this problems
682. 35:36especially if they are using our
683. 35:38PowerPoint presentations. Okay, so
684. 35:40that's it for today. Thank you for
685. 35:41listening and I hope to see you again on
686. 35:43the next video. God bless and bye-bye
687. 35:47for now.
688. 35:50Please click the subscribe button to
689. 35:52support this channel [music]
690. 35:57lessons. [music]
691. 36:07God bless [music] and see you on the
692. 36:10next video. Bye-bye.