SOLUTION: Solve |-10x + 70| = |8x - 74| I really have no idea as to how to go about starting this problem.... Please help!

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Question 150824: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!
Found 3 solutions by Fombitz, josmiceli, ankor@dixie-net.com:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28-10x%2B70%29=abs%288x-74%29
Absolute value problems are typically two problems in one (positive and negtive solution).
That's because abs%28x%29=x if x>0 and abs%28x%29=-x if x<0.
With an absolute value sign on each side, it now becomes 4 equations to solve.\
1. Positive=Positive
2. Positive=Negative
3. Negative=Positive
4. Negative=Negative
Luckily, if you look at the equations, 1 and 4 are the same, and 2 and 3 are the same.
That is, if I multiply both sides of 1 by (-1), I get 4, and the same for 2 and 3.
So you really only have to solve two equations, we'll call them A and B.
A.%28-10x%2B70%29=%288x-74%29
B.%28-10x%2B70%29=-%288x-74%29
Let's start with A,
A.-10x%2B70=8x-74
-18x=-144
highlight%28x=8%29
and then B,
B.-10x%2B70=-%288x-74%29
-10x%2B70=-8x%2B74%29
-2x=4%29
highlight%28x=-2%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28-10x+%2B+70%29+=+abs%288x+-+74%29
My algebra book tells me this equation is true if both
-10x+%2B+70+=+%2B%288x+-+74%29 and
-10x+%2B+70+=+-%288x+-+74%29 are true
I'll solve the 1st one
-10x+%2B+70+=+8x+-+74
18x+=+70+%2B+74
18x+=+144
x+=+8
And the second one,
-10x+%2B+70+=+-8x+%2B+74
2x+=+-4
x+=+-2
To check, I'll plug these back into the original equation
abs%28-10x+%2B+70%29+=+abs%288x+-+74%29
abs%28-10%2A8+%2B+70%29+=+abs%288%2A8+-+74%29
abs%28-10%29+=+abs%28-10%29
10+=+10
OK
Also,
abs%28-10x+%2B+70%29+=+abs%288x+-+74%29
abs%28-10%2A%28-2%29+%2B+70%29+=+abs%288%2A%28-2%29+-+74%29
abs%2890%29+=+abs%2890%29
90+=+90
OK
x = 8 and x = -2 are the solutions

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve |-10x + 70| = |8x - 74|
:
Case 1:
-10x + 70 = +|8x - 74|
-10x + 70 = 8x - 74
-10x - 8x = -74 - 70
-18x = -144
x = %28-144%29%2F%28-18%29
x = +8
;
Case 2:
-10x + 70 = -|8x - 74|
-10x + 70 = -(8x - 74)
-10x + 70 = -8x + 74
-10x + 8x = 74 - 70
-2x = +4
x = 4%2F%28-2%29
x = -2
:
Prove that this is true by substituting both values in the original equation
x=8)
|-10(8) + 70| = |8(8) - 74|
|-80 + 70| = |64 - 74|
|-10| = |-10|
+10 = +10
:
x=-2
|-10(-2) + 70| = |8(-2) - 74|
|+20 + 70| = |-16 - 74|
|+90| = |-90|
+90 = +90
: