## anonymous one year ago Need help with 15 8th grade questions. Will medal and fan!

1. anonymous

2. anonymous

What is the solution to the equation?

3. anonymous

-18+4+x=9-19 x=

4. anonymous

so keep x on one side and move all the the other number to the other... you should end up with x=9-19+18-4, add them all up and there you have it :D

5. anonymous

So, 4?

6. anonymous

@Emeyluv99

7. anonymous

4x-26-3x=16-20 x=

8. anonymous

thats right

9. anonymous

now for this second one, keep all the x's on one side and move everything else to the other

10. anonymous

4-26-3=16-20? @emeyluv99

11. anonymous

hang on, where are your x's you should be getting 4x-3x= 16-20+26

12. anonymous

I don't know. I'm confused :x I don't understand this.

13. anonymous

ok so you want to figure out the value of x. Yes?

14. anonymous

Correctumundo.

15. anonymous

so you have two numbers that are multiples of x, but, because you dont know what x is, you dont know what 4x or 3x is.

16. anonymous

Yes.

17. anonymous

so now, what we can do is put all the numbers that we know the value of (ie all the number that are not multiples of x) on one side, and keep the multiples of x on the other

18. anonymous

this just helps us see what we do and dont know and makes it easier to solve.

19. anonymous

20. anonymous

So, 4x-3x= 16-20+26

21. anonymous

@Emeyluv99

22. anonymous

good.

23. anonymous

I just copied what you put earlier....xd

24. anonymous

so now, what do you think 4x-3x is

25. anonymous

(ahah cheeky)

26. anonymous

I don't know!~ I am SO confused. No matter how it gets explained I don't understand.

27. anonymous

ok lets try some experimenting then shall we?

28. anonymous

We shall.

29. anonymous

so lets pretend that x=5.

30. anonymous

whats 3*5-4*5

31. anonymous

5

32. anonymous

NO!

33. anonymous

-5

34. anonymous

yes, youre correct

35. anonymous

its - 5

36. anonymous

15-20= -5

37. anonymous

now try with x=20. whats 4*20-3*20

38. anonymous

20

39. anonymous

good

40. anonymous

how about when x=30? whats 4*30-3*30?

41. anonymous

120-90=30

42. anonymous

I get this part.

43. anonymous

ae you seeing a pattern here?

44. anonymous

Yes.

45. anonymous

so theres this rule in algebra. It goes somehting like this: ax+bx =(a+b)x

46. anonymous

here a can be any number and b can be any number. id either of them are negative, that meass youre subtracting.

47. anonymous

in your case, a is 4 and b is -3. see if you can work out what 4x-3x is with this rule

48. anonymous

|dw:1442034277690:dw|

49. anonymous

pardon! IF either of them are negative that MEANS you're subtracting

50. anonymous

So, 16-9?

51. anonymous

not quite. Using the rule you should get that 4x-3x= (4-3)x. which is just x.

52. anonymous

..where is a and b?

53. anonymous

like x a and b are variables.. so depending on the problem a and b can be any number

54. anonymous

so in this problem, a= 4 and b=-3.

55. anonymous

So, a and b in this problem was 4 and -3. So, it would actually be, 4x-3x= (4-3)x

56. anonymous

exactly!

57. anonymous

Just copied what you said earlier :x

58. anonymous

haha, but do try to understand it.. it helps a LOT when you get into harder algebra.

59. anonymous

How would it equal (4-3)x?

60. anonymous

I GET IT!

61. anonymous

We moved the x to one side leaving only 4-3!1!

62. anonymous

YES! so now that means (4-3)x = x

63. anonymous

So 1= x?

64. anonymous

NO

65. anonymous

thats getting a little far ahead. Bring back the equation we made earlier.

66. anonymous

(4-3)x = x

67. anonymous

4x-3x= 16-20+26

68. anonymous

so what you have done is solved the left side of the equation. But, you cant ignore the right side!

69. anonymous

We know that 4x-3x=x right?

70. anonymous

Yes.

71. anonymous

so what we do now, because x and 4x-3x have the SAME VALUE, we can say x= 16-20+26

72. anonymous

So, x=22?

73. anonymous

exactly!

74. anonymous

I'm going to try ONE on my own. Stay here though, so you can tell me if I'm wrong.

75. anonymous

sure thing!

76. anonymous

The one I'm trying is -4x=5(x-2)=-16+10

77. anonymous

go for it

78. anonymous

Would the beginning be -4+5(-2)=-16+10xx?

79. anonymous

hm.. not quite.

80. anonymous

the thing is you have two equations here. take one at a time. start with -4x= 5(x-2) and then move on to 5(x-2) = -16+10

81. anonymous

OK.

82. anonymous

:( Confused now. T_T I REALLY want to get this! I just can't understand.

83. anonymous

and also, remember the rule i showed you before? you'll have to use that here, but in reverse. Youll be doing (a+b)x= ax+bx

84. anonymous

the hardest part in this is unravelling 5(x-2)

85. anonymous

(-4+5)x=-4x+5x?

86. anonymous

@Emeyluv99

87. anonymous

exactly like that, but do that with the numbers you have in this equation. remember that a and b change depending on what your equation is.

88. anonymous

Aren't a and b --5 and 5?

89. anonymous

so if the rule is x(a+b), here, your x=5, a=x and b=-2. But this does not mean that your answer is x! because you ahve a whole other equation to solve!

90. anonymous

(x+-2)5=-2*5+x*5

91. anonymous

??

92. anonymous

excellent!

93. anonymous

so lets bring back the first of our two equation. -4x= 5(x-2)

94. anonymous

you know what the 5(x-2) is now. so go ahead and replace that with what we found out with the rule

95. anonymous

Wait what? Replace what?

96. anonymous

so we found out that 5(x-2) = -2*5 + x*5 right?

97. anonymous

Yes.

98. anonymous

ok so, we know that both 5(x-2) and -2*5 +x*5 have the SAME VALUE

99. anonymous

so whats stopping us from writing -4x= 5(x-2) as -4x= -2*5+x*5 ?

100. anonymous

T_T I understand when you write it, but not how you got it! :(

101. anonymous

lets make an analogy ok?

102. anonymous

Yes ma'am.

103. anonymous

oh please dont ma'am me, im only 15 ahah

104. anonymous

I know, but you're my teacher (senpai), so you are ma'am.

105. anonymous

hahah very well then!

106. anonymous

but lets say we have we have a banana and two apples

107. anonymous

Yes ma'am!

108. anonymous

lets name this banana -4x

109. anonymous

*laughs* OK...

110. anonymous

now one of our apples is called 5(x-2) and we find out that the other one (called -2*5+x*5) has the exact same weight!

111. anonymous

Yes ma'am! (making a sandwich, but keep explaining.)

112. anonymous

Back.

113. anonymous

so we put apple 5(x-2) and banana -4x on a set of scales and we see that they have the same weight

114. anonymous

now because we know that apple 5(x-2) and apple -2*5+x*5 have the same weight, we replace apple 5(x-2) with apple -2*5+x*5

115. anonymous

and what do you think we find between this new apple and the banana?

116. anonymous

There's a weight difference?

117. anonymous

ah remember that both apples have the same weight! so technically, switching them around makes no difference

118. anonymous

OH! I get it!(nope)

119. anonymous

say we take two different bags of flower same weight same everything

120. anonymous

and we compare it to a brick of equal weight.

121. anonymous

So everything is the same?

122. anonymous

yes so if everything is the same,

123. anonymous

the weight difference between bag 1 and the brick is 0, and the weight difference between bag 2 and the brick is?

124. anonymous

0

125. anonymous

exaclty so if both bags are the same, does it matter which one we compare it to?

126. anonymous

Not at all ma'am.

127. anonymous

similarly, 5(x-2) and -2*5+x*5 are have exactly the same "weight" (mathematically its value, but we'll say weight until you get the hang of it)

128. anonymous

so does it matter which one we compare to -4x?

129. anonymous

No ma'am.

130. anonymous

so we choose to compare it to -2*5+x*5 because its easier to work with

131. anonymous

which is why we had gotten -4x= -2*5+x*5

132. anonymous

What is 'it' Ms. Luv?

133. anonymous

'it" is -4x

134. anonymous

OH!

135. anonymous

im sensing a eureka moment!

136. anonymous

so now we can take care of one of the two equations we made! -4x= -2*5+x*5 so get all the x's to one side and all the non x's to the other just like we did before

137. anonymous

Eureka!! I still don't understand! (keep explaining)

138. anonymous

remember it doesnt matter which one (5(x-2) or -2*5+x*5) we compare -4x to, we choose the second option because its easier for us to solve

139. anonymous

Ugghh! MY BRAIN IS BUILT FOR ENGLISH, NOT MATH!!!

140. anonymous

ahahah mines the otherway around. keep trying

141. anonymous

i have to run to lunch give me 20 minutes please. keep trying ill be back soon!

142. anonymous

Will do!

143. anonymous

So, -30?@Mimi_x3 @j2lie

144. anonymous

@Mimi_x3

146. anonymous

-4x=5(x-2)=-16+10

147. anonymous

x=?

|dw:1442038760084:dw|

149. anonymous

so 32

150. anonymous

@Emeyluv99

|dw:1442038811837:dw|

no |dw:1442038932820:dw|

|dw:1442038977386:dw|

@ShirouxGhoul do you understand

155. anonymous

No...not yet. Help with a few more?

say

157. anonymous

No...not yet. Help with a few more?

yes

159. anonymous

-6.8+2.6+x=9.7 x=?

160. anonymous

hey i'm back... if you still need help :D

161. anonymous

I wish @Emeyluv99 was back! I ..EMEY!!!!!!

|dw:1442039191373:dw|

163. anonymous

hello! your wish is granted ahah

164. anonymous

so where are we now?

165. anonymous

Emey, I don't do good with word problems, so please use a standard problem.

166. anonymous

-6.8+2.6+x=9.7

167. anonymous

got it.

|dw:1442039271587:dw|

170. anonymous

this is exactly like that first problem we did. move everything without x to one side and add em all up !

171. anonymous

OK! Thank you so mcuh @madhu.mukherjee.946!! Tell me if you need help!

172. anonymous

Hmm, we're polar opposites....

173. anonymous

alrighty then @ShirouxGhoul, where are we

174. anonymous

we do seem to be dont we.. ahah

175. anonymous

-6.8+2.6+x=9.7

176. anonymous

ah yes. so lets get everything that doesnt have x on one side, like we did before.

177. anonymous

that would give us x=9.7+6.8-2.6

178. anonymous

-4.2

179. anonymous

13.9

180. anonymous

yup

181. anonymous

x=13.9?!

182. anonymous

the trick to any algebra problem like the one's were doing right now is to always try and get x (or any other variable) alone on one side.

183. anonymous

x=13.9?!

184. anonymous

it is

185. anonymous

The problem is done...?

186. anonymous

yup

187. anonymous

*mindblow*

188. anonymous

hahaha see, x is antisocial and wants all the number to leave his side and go to the other side.

189. anonymous

OMEGERD! It's SO complicated now!!

190. anonymous

whats the next one? we'll get through this, hang in there!

191. anonymous

1/3x+ 1/3 (2x-15) =3 1/2

192. anonymous

x= blank blank over blank

193. anonymous

ah fractions!

194. anonymous

Mixed number I believe.

195. anonymous

first tip to understand agebra with fractions, what does it mean when something is a fraction?

196. anonymous

It's a part?

197. anonymous

Of a whole?

198. anonymous

yes so what are you doing to the whole to find that part. Adding? multiplying? Dividing or subracting?

199. anonymous

Dividing, I believe.

200. anonymous

correct.

201. anonymous

are you familiar with the order of operations?

202. anonymous

Yes!

203. anonymous

Pemdas?

204. anonymous

excellent! its going to make your life SO much easier here

205. anonymous

I hope so!

206. anonymous

oh hang on a second. this is different

207. anonymous

scratch that sorry i read that wrong.

208. anonymous

ok new board.

209. anonymous

so when you have fractions in algebra, you reallly want to get rid of the denominators. How do you think you do that?

210. anonymous

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions?

211. anonymous

good!

212. anonymous

Don't you just LOVE Google? ;x

213. anonymous

i really do!

214. Jhannybean

This is quite a long thread you have going :o

215. anonymous

so when we have this in algebra, what we do is multiply EVERYTHING in the equation by BOTH denominators.

216. anonymous

Well, since I Googled it, I get it now. (The denominator thing, not this thing)

217. anonymous

so it will look somehthing like this.

218. anonymous

@Jhannybean It's because I'm stupid, and it's impossible to explain things to me. :~

219. Jhannybean

I mean... if that's what you want to believe....

220. anonymous

@ShirouxGhoul You're not stupid! Dont say that! You'e brains just hardwired for English!

221. anonymous

besides, you'll get the hang of algebra in time!

222. anonymous

.....

223. Jhannybean

Any other questions @ShirouxGhoul ? I can also give it a try! :)

224. anonymous

$$\frac{1}{3x}+ \frac{1}{3 (2x-15)} =3 \frac{1}{2}$$ $$(3(2x-15))(3x) \frac{1}{3x} + (3(2x-15))(3x) \frac{1}{3(2x-15)} = (3(2x-15))(3x) \frac{7}{2}$$

225. anonymous

the second is what you get when you multiply the whole equation by both denominators on the right side!

226. Jhannybean

whoah, thats too many steps all muddled into one.

227. anonymous

true, let me break it down.

228. Jhannybean

first and foremost, simplify everything. all fractions.

229. anonymous

write 3 1/2 as an improper fraction first, it makes it easier to visualise everything

230. Jhannybean

$\sf 3\frac{1}{2} \implies \frac{(3\cdot 2)+1}{2} =~?$

231. anonymous

after you figure that out, choose one denominator, to get rid of. one at a time, we can get rid of all of them.

232. anonymous

Internet went out for a min. Sorry!

233. anonymous

no problem! so make the improper fraction and choose a denominator to eliminate first! we'll continue from there!

234. Jhannybean

That's true, @Emeyluv99 , or you can look at $$\sf 3x$$ , $$\sf 3(2x-15)$$ and $$\sf 2$$ and multiply both the numerator and denominator of each fraction with the multiplication between all 3 of these.

235. anonymous

WHOA! Slow down! I am SO confused! You have to remember, i don't understand this all too well.

236. anonymous

yes, lets take this one by one.

237. anonymous

*I

238. Jhannybean

Ok, ok, sorry!! I was referencing @Emeyluv99 :)

239. anonymous

so @ShirouxGhoul already told me that the way to get rid of a denominator is to multiply the fraction.

240. Jhannybean

Thats correct

241. anonymous

so lets start one at a time. Well do 3x first

242. anonymous

because we're dealing with an equation, we have to multiply EVERYTHING with 3x, not just that fraction. so that'll give us $$(3x) \frac{1}{3x}+(3x) \frac{1}{3(2x−15)}=(3x) \frac{7}{2}$$

243. anonymous

in our first fraction, 3x cancels out with 3x, so it just becomes 1

244. anonymous

@Jhannybean It's OK, I was just saying I was lost is all. :)

245. anonymous

did you get that last bit?

246. anonymous

Yes. So now we're left with 1 in place of x?

247. anonymous

we're left with 1 in place of $\frac{1}{3x}$

248. anonymous

$$1+(3x) \frac{1}{3(2x−15)}=(3x) \frac{7}{2}$$

249. anonymous

do you see what i mean?

250. anonymous

I think so.

251. anonymous

@Emeyluv99???

252. anonymous

yes im here, the internet 's being mean sorry

253. anonymous

3(2x-15). We'll multiply everything in the equation by this to get: $$(3(2x-15)) 1 + (3(2x-15)) (3x) \frac{1}{3(2x-15)} = (3(2x-15)) (3x) \frac{7}{2}$$

254. Jhannybean

Found the reason for the lag, 1. thread is WAY too long 2. it's taking a lot of time to load the latex. TRy opening a new question after you guys are done. Makes things easier.

255. anonymous

@Jhannybean that makes a lt of sense.. thanks so much!