|x-2|=2 — step-by-step solution | Explain MAths

|x-2|=2

Let's solve in

ℝ

:

| x - 2 | = 2

Since

2 \geq 0

,

| x - 2 | = 2

is equivalent to

x - 2 = 2

or

x - 2 = -2

Let's solve in

ℝ

:

x - 2 = 2

ⓘ We add

2

to both sides

x = 2 + 2

ⓘ Start from

2

and move forward

2

on the number line:

2 + 2

=

4

Solution found:

x = 4

Let's solve in

ℝ

:

x - 2 = -2

ⓘ We add

2

to both sides

x = - 2 + 2

ⓘ Start from

-2

and move forward

2

on the number line, up to zero:

- 2 + 2

=

0

Solution obtained:

x = 0

▶Solution:

x = {0, 4}