4|y+4|-8=0 — step-by-step solution | Explain MAths

4|y+4|-8=0

Let's solve in

ℝ

:

4 \cdot | y + 4 | - 8 = 0

ⓘ We add

8

to both sides

4 \cdot | y + 4 | = 8

Since

4 \neq 0

, divide both sides by

4

:

| y + 4 | = 2

Since

2 \geq 0

,

| y + 4 | = 2

is equivalent to

y + 4 = 2

or

y + 4 = -2

Let's solve in

ℝ

:

y + 4 = 2

ⓘ We subtract

4

from both sides

y = 2 - 4

ⓘ Start from

2

and move back

4

on the number line, going below zero:

2 - 4

=

-2

Solution found:

y = -2

Let's solve in

ℝ

:

y + 4 = -2

ⓘ We subtract

4

from both sides

y = - 2 - 4

ⓘ Start from

-2

and move back

4

more on the number line, away from zero:

- 2 - 4

=

-6

Solution found:

y = -6

▶Solution:

y = {-6, -2}