sqrt(x-1)>2 — step-by-step solution

Let's solve in

ℝ

\sqrt{x - 1} > 2

Isolate the square root:

\sqrt{x - 1} > 2

. Since both sides are nonnegative, square both sides, which keeps the direction of the inequality:

x - 1 > 2^{2}

ⓘ An integer power is a repeated product:

2^{2}

2 \cdot 2

4

x - 1 > 4

ⓘ We add

1

to both sides

x > 4 + 1

ⓘ Start from

4

and move forward

1

on the number line:

4 + 1

5

Candidates, pending the domain check:

x > 5

Let's find the domain of

\sqrt{x - 1} > 2

For the expression

\sqrt{x - 1}

to exist, you must check:

x - 1 \geq 0

ⓘ We add

1

to both sides

Domain constraints:

x \geq 1

▶Solution:

x > 5