## anonymous 5 years ago -17 – x = -2(3x + 1)

1. anonymous

You need to distribute the -2 to each of the terms in the parentheses. Then you can solve it in the usual way.

2. anonymous

i did that polPak and heres what i came up with

3. anonymous

-21

4. anonymous

Nope. What was the equation after you do the distributing?

5. anonymous

-17 - 6x +6X -2-X

6. anonymous

2(3X +1) -17- X= 6X + 2

7. anonymous

You forgot that it's a -2, not 2 you're distributing.

8. anonymous

$-2(3x + 1) = -2(3x) -2(1) = -6x - 2$ So you should have $17 - x = -6x -2$

9. anonymous

oh so the 6 becomes -6x

10. anonymous

And the 2 becomes -2.

11. anonymous

Err My equation is slightly wrong.. You should have $-17 -x = -6x -2$

12. anonymous

-17 - x = -6 - 2

13. anonymous

Don't lose track of the x on the -6. It's important

14. anonymous

then now i can solve for x so the its -17x -6 - 2

15. anonymous

No. -17 - x is not -17x and you can't just put them together like that.

16. anonymous

Ok look at it like this.

17. anonymous

ok

18. anonymous

You have this equation: $-17 - x = -6x -2$ That means that $$-17 - x$$ IS EXACTLY THE SAME AS $$-6x -2$$ So if they are the same then isn't $$(-6x -2) + 2$$ exactly the same as $$(-17 - x) + 2$$?

19. anonymous

-17 - 8 so there for x is 8

20. anonymous

I have no idea what you are doing.. -17 - 8 doesn't enter into it.

21. anonymous

i am just lost

22. anonymous

Ok stop doing things.. Just look at what I'm saying.

23. anonymous

$-17 - x \text{ EQUALS } -6x -2$

24. anonymous

okay lol i am stopping right now

25. anonymous

Ok? They are the same.

26. anonymous

That's what equals means right?

27. anonymous

yes

28. anonymous

Ok so now lets use some basic arithmetic rules to clean this up a bit. First we can swap the terms on the left because addition can be rewritten in any order and it works the same.. $-17 -x = -x -17$ right?

29. anonymous

okay

30. anonymous

Do you agree that those two are equal? Is 3+5 the same as 5+3 and -3 - 5 the same as -5 - 3?

31. anonymous

yes

32. anonymous

because you distribute right

33. anonymous

Commute, but yeah.

34. anonymous

Ok, so -17 - x is the same as -x - 17. But we also said that -17 - x was the same as -6x - 2. So that means that -x - 17 must be the same as -6x - 2.

35. anonymous

Right?

36. anonymous

right

37. anonymous

So now our equation looks like this: $-x - 17 = -6x - 2$

38. anonymous

that part i got is solving for x thats has me upside ways

39. anonymous

We'll get there.

40. anonymous

So if those two things are the same.. Then isn't $6x + (-x - 17) = 6x + (-6x - 2)$

41. anonymous

Because we added 6x to both sides, and if they were equal to start with, they must still be equal.

42. anonymous

okay thats the part that throws me off

43. anonymous

How so?

44. anonymous

its like my flipping mind goes blank and i have no idea what comes next

45. anonymous

Ok relax for a second and lets talk about something else first.

46. anonymous

or maybe i am trying too hard to understand and i get tied up

47. anonymous

Think of a number, any number you want. Don't tell me what it is.

48. anonymous

ok

49. anonymous

Now, tell me what 2 times that number is.

50. anonymous

184

51. anonymous

Ok. So now I will magically read your mind and tell you that your number is 92!

52. anonymous

How did I accomplish this sorcery?

53. anonymous

lol yes

54. anonymous

you divided

55. anonymous

But how does that help me?

56. anonymous

Because you told me that 2x = 182

57. anonymous

Well I know that if 2x = 182 then $2x \times {1 \over 2} = 182 \times {1 \over 2}$

58. anonymous

so you have to find out what 2x amounts to

59. anonymous

Because you said that they were the same, so anything I do to both sides will maintain equality.

60. anonymous

And $2x \times \frac{1}{2} = x$

61. anonymous

And $182 \times \frac{1}{2} = 92$

62. anonymous

So therefore x = 92

63. anonymous

So now I'm thinking of a number.

64. anonymous

91

65. anonymous

okay

66. anonymous

Whoops. Sorry I typo'd your response.

67. anonymous

Shoulda been 184 not 182.

68. anonymous

no one has ever broke it down like this thank you

69. anonymous

its okay

70. anonymous

so you want me to solve for your number

71. anonymous

Now if you take the number I'm thinking of, and add 17 to it. You will get 2 more than 6 times that same number.

72. anonymous

So first. can you write an equation (using x for my number) which describes the statement I've given you?

73. anonymous

2(6^6)+17=X

74. anonymous

Not quite. Lets break down what I said: x + 17 The number I'm thinking of, and add 17 to it = IS 2 more than 6 times that number 2 + 6x

75. anonymous

Or better still 6x + 2

76. anonymous

12(6)=72+17=89

77. anonymous

No no no.

78. anonymous

OH WOW

79. anonymous

80. anonymous

okay am slowing down

81. anonymous

and laughing at myself

82. anonymous

np =)

83. anonymous

Try again. 14 more than the number is 2 more than 4 times the number.

84. anonymous

We're just practicing turning english into equations.

85. anonymous

okay

86. anonymous

Don't try to solve it yet. Just rewrite what I say in equation form.

87. anonymous

Actually 14 more than the number is 5 more than 4 times the number.

88. anonymous

14 + n = 2(4)

89. anonymous

Sorry

90. anonymous

Almost!

91. anonymous

was i close

92. anonymous

The left side is right, the right side is not.

93. anonymous

Try my last version, but break it down a bit. If x is my number what is 4 times my number??

94. anonymous

14 + n = 5(4 + n) oh please be right

95. anonymous

You're doing great btw. It's important to have patience when working through this.

96. anonymous

No, that's not right still. Lets work through it a little at a time.

97. anonymous

What is 4 times my number?

98. anonymous

99. anonymous

no

100. anonymous

my number is x

101. anonymous

ok am gonna shoot here is it 14x be gentel

102. anonymous

lets do something really quick cause it seems like we have a breakdown when you try to use letters instead of numbers. If I tell you my number is 22, and I ask what is 2 times my number what would you do?

103. anonymous

2(22)=44

104. anonymous

Awsome!

105. anonymous

That's perfect

106. anonymous

Now if I tell you my number is k and I ask you what's 4 times my number what would you do?

107. anonymous

yeah me finally

108. anonymous

4(k)

109. anonymous

yep!

110. anonymous

And if I tell you my number is b and I ask what is 5 more than (4 times my number)?

111. anonymous

You taking a long time, so I know something is wrong ;p

112. anonymous

If I tell you my number is 3 and I ask what is 5 more than my number?

113. anonymous

oh help me okay it would 20(b) or 5(b)=20

114. anonymous

neither.

115. anonymous

darn it

116. anonymous

it's just a little language barrier. We'll fix it

117. anonymous

If I tell you my number is 3 and I ask what is 5 more than my number what would you do?

118. anonymous

am trying not to think of the words

119. anonymous

the words are important.

120. anonymous

3(5)=15

121. anonymous

15 is 3 more than 5?

122. anonymous

Or 5 more than 3?

123. anonymous

What is 5 more than 3?

124. anonymous

8

125. anonymous

5 + 3

126. anonymous

127. anonymous

5 + 3 means 5 more than 3

128. anonymous

gosh i feel stupid now

129. anonymous

It's ok. Just a little gap in your knowledge.

130. anonymous

so am mixing up more with multiplying

131. anonymous

a huge gap

132. anonymous

Right. If I say 4 times my number is 4k Then what is 5 more than 4 times my number?

133. anonymous

ok let me solve it

134. anonymous

Don't have to solve, just have to translate.

135. anonymous

4k +9

136. anonymous

So close!

137. anonymous

oops i left off the 4

138. anonymous

No.

139. anonymous

Ok, my number is k. What is 4 times my number?

140. anonymous

4(k)=4k

141. anonymous

Ok, and what is 5 more than 4 times my number?

142. anonymous

You already solved half of this just a minute ago.

143. anonymous

9(n)

144. anonymous

holding my breath

145. anonymous

No. it's 5 + 4k 5 more than four times my number

146. anonymous

5 + 4k

147. anonymous

5 more means +5

148. anonymous

am trying too hard

149. anonymous

yes

150. anonymous

Ok, but now you know.

151. anonymous

okay so i don't add 5 and 4 just 5+ 4k

152. anonymous

right

153. anonymous

these are the steps. -17-x=-6x-2 6x-x=17-2 5x=15 x=3

154. anonymous

While I'm sure doing her work is appreciated it's not going to help her on the next problem.

155. anonymous

awe man

156. anonymous

thats true

157. anonymous

thanks pat18

158. anonymous

One sec Bella. This thread is lagging up a bit. Lets start a new question with the next one?

159. anonymous

okay

160. anonymous

brb

161. anonymous

you are welcome.

162. anonymous

okay am back polPak

163. anonymous

Can you make a new questiON?

164. anonymous

err question?

165. anonymous

okay

166. anonymous

what is 6 times my number a and 8 more times 4

167. anonymous

Oh, sorry I think you misunderstand. I am going to make a new problem on the left side. Please go there