|x+3|>= 2 — step-by-step solution | Explain MAths

|x+3|>= 2

Let's solve in

ℝ

:

| x + 3 | \geq 2

| A | \geq B

means that:

A \geq B

or

A \leq - B

Let's solve in

ℝ

:

x + 3 \geq 2

ⓘ We subtract

3

from both sides

x \geq 2 - 3

ⓘ Start from

2

and move back

3

on the number line, going below zero:

2 - 3

=

-1

Solution obtained:

x \geq -1

Let's solve in

ℝ

:

x + 3 \leq -2

ⓘ We subtract

3

from both sides

x \leq - 2 - 3

ⓘ Start from

-2

and move back

3

more on the number line, away from zero:

- 2 - 3

=

-5

Solution obtained:

x \leq -5

▶Solution:

x \in (-∞, -5] \cup [-1, +∞)