(x+1)^2>4 — step-by-step solution | Explain MAths

(x+1)^2>4

Let's solve in

ℝ

:

{(x + 1)}^{2} > 4

An even power only depends on the absolute value:

{(x + 1)}^{2} > 4

is equivalent to

| x + 1 | > 2

| A | > B

means that:

A > B

or

A < - B

Let's solve in

ℝ

:

x + 1 > 2

ⓘ We subtract

1

from both sides

x > 2 - 1

ⓘ Start from

2

and move back

1

on the number line:

2 - 1

=

1

Solution obtained:

x > 1

Let's solve in

ℝ

:

x + 1 < -2

ⓘ We subtract

1

from both sides

x < - 2 - 1

ⓘ Start from

-2

and move back

1

more on the number line, away from zero:

- 2 - 1

=

-3

Solution found:

x < -3

▶Solution:

x \in (-∞, -3) \cup (1, +∞)