3|x-1|+2<= 8 — step-by-step solution

Let's solve in

ℝ

3 \cdot | x - 1 | + 2 \leq 8

ⓘ We subtract

2

from both sides

3 \cdot | x - 1 | \leq 8 - 2

ⓘ Start from

8

and move back

2

on the number line:

8 - 2

6

3 \cdot | x - 1 | \leq 6

Since

3 > 0

, divide both sides by

3

without reversing the inequality:

| x - 1 | \leq 2

| A | \leq B

is equivalent to

- B \leq A \leq B

-2 \leq x - 1 \leq 2

We add

1

to all three parts of the inequality

-1 \leq x \leq 3

▶Solution obtained:

x \in [-1, 3]