SOLUTION: Solve |-10x + 70| = |8x - 74|
I really have no idea as to how to go about starting this problem.... Please help!
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
Absolute value problems are typically two problems in one (positive and negtive solution).
That's because if x>0 and 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.
B.
Let's start with A,
A.
and then B,
B.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
My algebra book tells me this equation is true if both
and
are true
I'll solve the 1st one
And the second one,
To check, I'll plug these back into the original equation
OK
Also,
OK
x = 8 and x = -2 are the solutions
Answer by ankor@dixie-net.com(22740) (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 =
x = +8
;
Case 2:
-10x + 70 = -|8x - 74|
-10x + 70 = -(8x - 74)
-10x + 70 = -8x + 74
-10x + 8x = 74 - 70
-2x = +4
x =
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
:
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