Question

Solve the compound inequality 2x − 3 < 7 and 5 − x ≤ 8. A. x ≥ 3 and x < 2 B. x ≥ 3 and x < 5 C. x ≥ −3 and x < 2 D. x ≥ −3 and x < 5

Answer 1

Given:

The compound inequality $2x-3 < 7$ and $5-x \leq 8$.

To find:

The solution for the given compound inequality

Solution:

We have, compound inequality $2x-3 < 7$ and $5-x \leq 8$.

For $2x-3 < 7$,

Add 3 on both sides.

$2x < 7+3$

$2x < 10$

Divide 2 on both sides.

$x< 5$            ...(i)

For $5-x \leq 8$,

Subtract 5 from both sides.

$-x \leq 8-5$

$-x \leq 3$

Divide both sides by -1. So, the sign of inequality is changed.

$x \geq -3$            ...(ii)

Using (i) and (ii), we get the solution of given compound inequality as

$x \geq -3$  and $x< 5$

Therefore, the correct option is D.