|3x - 2| = 14.

Answer 1

To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 3x - 2 > 0
If 3x - 2 > 0, then we can remove the absolute value signs without changing the inequality:
3x - 2 = 14

Adding 2 to both sides:
3x = 16

Dividing both sides by 3:
x = 16/3

Case 2: 3x - 2 < 0
If 3x - 2 < 0, then we need to change the sign when removing the absolute value signs:
-(3x - 2) = 14

Expanding the expression:
-3x + 2 = 14

Subtracting 2 from both sides:
-3x = 12

Dividing both sides by -3:
x = -4

Therefore, the solutions to the equation |3x - 2| = 14 are x = 16/3 and x = -4.