Questions on Algebra: Absolute value answered by real tutors!

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

Answer by Fombitz(1756) About Me  (Show Source):
You can put this solution on YOUR website!
abs(-10x+70)=abs(8x-74)
Absolute value problems are typically two problems in one (positive and negtive solution).
That's because abs(x)=x if x>0 and abs(x)=-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.(-10x+70)=(8x-74)
B.(-10x+70)=-(8x-74)
Let's start with A,
A.-10x+70=8x-74
-18x=-144
highlight(x=8)
and then B,
B.-10x+70=-(8x-74)
-10x+70=-8x+74)
-2x=4)
highlight(x=-2)
Question 150824: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!
: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!

Answer by josmiceli(2035) About Me  (Show Source):
You can put this solution on YOUR website!
abs(-10x + 70) = abs(8x - 74)
My algebra book tells me this equation is true if both
-10x + 70 = +(8x - 74) and
-10x + 70 = -(8x - 74) are true
I'll solve the 1st one
-10x + 70 = 8x - 74
18x = 70 + 74
18x = 144
x = 8
And the second one,
-10x + 70 = -8x + 74
2x = -4
x = -2
To check, I'll plug these back into the original equation
abs(-10x + 70) = abs(8x - 74)
abs(-10*8 + 70) = abs(8*8 - 74)
abs(-10) = abs(-10)
10 = 10
OK
Also,
abs(-10x + 70) = abs(8x - 74)
abs(-10*(-2) + 70) = abs(8*(-2) - 74)
abs(90) = abs(90)
90 = 90
OK
x = 8 and x = -2 are the solutions
Question 150824: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!
: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!

Answer by ankor@dixie-net.com(4535) 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 = (-144)/(-18)
x = +8
;
Case 2:
-10x + 70 = -|8x - 74|
-10x + 70 = -(8x - 74)
-10x + 70 = -8x + 74
-10x + 8x = 74 - 70
-2x = +4
x = 4/(-2)
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
: