The set of x-values satisfying the inequality 2 |x-1| 5 is:

This inequality can be split into two inequalities: 2 x-15 or 21-x5. Solving for x gives 3 x6 or -4 x-1. -4 x-1 or 3 x 6

Browse · harp

smc

algebra senior

Problem

The set of

x

-values satisfying the inequality

2 \leq ∣ x - 1∣ \leq 5

is:

(A)

- 4 \leq x \leq - 1 or 3 \leq x \leq 6

(B)

3 \leq x \leq 6 or - 6 \leq x \leq - 3

(C)

x \leq - 1 or x \geq 3

(D)

- 1 \leq x \leq 3

Solution

This inequality can be split into two inequalities:

2 \leq x - 1 \leq 5

2 \leq 1 - x \leq 5

. Solving for x gives

3 \leq x \leq 6

- 4 \leq x \leq - 1

- 4 \leq x \leq - 1 or 3 \leq x \leq 6

Final answer