Question

What is the solution of |5x + 1|+ 6 = 21?

Answer 1

5|x + 1| + 6 = 21

5|x + 1| = 15

|x + 1| = 3

Recall the definition of absolute value: |x| = +x if x ≥ 0, and |x| = -x if x < 0.

This means

• if x + 1 ≥ 0, or x ≥ -1, then |x + 1| = x + 1, and so

x + 1 = 3

x = 2, or

• if x + 1 < 0, or x < -1, then |x + 1| = -(x + 1), and so

-(x + 1) = 3

x + 1 = -3

x = -4