(x/2+1)^2<=4 — step-by-step solution

Let's solve in

ℝ

{(\frac{x}{2} + 1)}^{2} \leq 4

An even power only depends on the absolute value:

{(\frac{x}{2} + 1)}^{2} \leq 4

is equivalent to

| \frac{x}{2} + 1 | \leq 2

| A | \leq B

is equivalent to

- B \leq A \leq B

-2 \leq \frac{x}{2} + 1 \leq 2

We add

-1

to all three parts of the inequality

-3 \leq \frac{x}{2} \leq 1

We divide all three parts by

\frac{1}{2}

, which is positive

-6 \leq x \leq 2

▶Solution obtained:

x \in [-6, 2]