<PRE><B>Question 150824</B>
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
:
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