4<=|2x-8| — step-by-step solution

1) We solve in

ℝ

| 2 x - 8 | \geq 4

From

| A | \geq B

, we deduce:

A \geq B

A \leq - B

2) We solve in

ℝ

2 x - 8 \geq 4

ⓘ Add

8

to both sides

2 x \geq 4 + 8

ⓘ Start from

4

and move forward

8

on the number line:

4 + 8

12

2 x \geq 12

ⓘ Both sides are divided by

2

x \geq \frac{12}{2}

ⓘ Simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{12}{2}

6

Solution found:

x \geq 6

3) Let's solve in

ℝ

2 x - 8 \leq -4

ⓘ We add

8

to both sides

2 x \leq - 4 + 8

ⓘ Start from

-4

and move forward

8

on the number line, going past zero:

- 4 + 8

4

2 x \leq 4

ⓘ Divide both sides by

2

x \leq \frac{4}{2}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{4}{2}

2

Solution found:

x \leq 2

▶Solution:

x \in (-∞, 2] \cup [6, +∞)