|4(x-1)+10|<= 14 — step-by-step solution

Let's solve in

ℝ

| 4 \cdot (x - 1) + 10 | \leq 14

ⓘ We subtract

0

from both sides■Expand by multiplying each term inside the parentheses:

4 \cdot (x - 1)

4 x - 4

| 4 x - 4 + 10 | \leq 14

ⓘ Start from

-4

and move forward

10

on the number line, going past zero:

- 4 + 10

6

| 4 x + 6 | \leq 14

| A | \leq B

is equivalent to

- B \leq A \leq B

-14 \leq 4 x + 6 \leq 14

We add

-6

to all three parts of the inequality

-20 \leq 4 x \leq 8

We divide all three parts by

4

, which is positive

-5 \leq x \leq 2

▶Solution obtained:

x \in [-5, 2]