4|x-1|-8<= 40 — step-by-step solution

Let's solve in

ℝ

4 \cdot | x - 1 | - 8 \leq 40

ⓘ We add

8

to both sides

4 \cdot | x - 1 | \leq 40 + 8

ⓘ Start from

40

and move forward

8

on the number line:

40 + 8

48

4 \cdot | x - 1 | \leq 48

Since

4 > 0

, divide both sides by

4

without reversing the inequality:

| x - 1 | \leq 12

| A | \leq B

is equivalent to

- B \leq A \leq B

-12 \leq x - 1 \leq 12

We add

1

to all three parts of the inequality

-11 \leq x \leq 13

▶Solution obtained:

x \in [-11, 13]