Question

Solve |2 - 3x| = 7.
A. {-5/3, 3}
B. {-15, 3}
C. {-3, 5/3}
D. {-3, 15}

Answer 1

|x| is the same thing as |-x| by the definition of absolute value. So,
|2 - 3x| = 7 is the same thing as |-(2 - 3x)| = 7.

To solve this we get rid of the absolute value signs and turn it into two problems.
|2 - 3x| = 7
|-(2 - 3x)| = 7

2 - 3x = 7
-2
-3x = 5
/-3
x = 5/-3

|-(2 - 3x)| = 7
-(2 - 3x) = 7
-2 + 3x = 7
+2
3x = 9
/3
x = 3

x = 3, (5/-3)

A.