|x-5|>= 3 — step-by-step solution | Explain MAths

|x-5|>= 3

Let's solve in

ℝ

:

| x - 5 | \geq 3

| A | \geq B

means that:

A \geq B

or

A \leq - B

Let's solve in

ℝ

:

x - 5 \geq 3

ⓘ We add

5

to both sides

x \geq 3 + 5

ⓘ Start from

3

and move forward

5

on the number line:

3 + 5

=

8

Solution found:

x \geq 8

Let's solve in

ℝ

:

x - 5 \leq -3

ⓘ We add

5

to both sides

x \leq - 3 + 5

ⓘ Start from

-3

and move forward

5

on the number line, going past zero:

- 3 + 5

=

2

Solution obtained:

x \leq 2

▶Solution:

x \in (-∞, 2] \cup [8, +∞)