Question

The solution set for the inequation – 2x + 7 ≤ 3, x ∈ R is ______.

Options

• {x : x ∈ R, x < 2}

• {x : x ∈ R, x > 2}

• {x : x ∈ R, x ≤ 2}

• {x : x ∈ R, x ≥ 2}

Answer 1

The solution set for the inequation – 2x + 7 ≤ 3, x ∈ R is {x : x ∈ R, x ≥ 2}.

Explanation:

Given – 2x + 7 ≤ 3

`\implies` – 2x ≤ 3 – 7

`\implies` – 2x ≤ – 4

`\implies` 2x ≥ 4  ...[If a < b, c < 0 `\implies` ac > bc]

`\implies` x ≥ 2, x ∈ R

∴ Solution set = {x : x ∈ R, x ≥ 2}