Question

Solve the system of inequalities: $2x+5\le 0,x-3\le 0$.

• A. $x\ge -\frac{5}{2}$
• B. $x\le \frac{5}{2}$
• C. $x\le -\frac{5}{2}$
• D. $x\ge \frac{5}{2}$

Answer 1

The correct option is C $x\le -\frac{5}{2}$

Given $2x+5\le 0$

Add $-5$ on both sides, we get

$2x+5-5\le 0-5$

$\Rightarrow 2x\le -5$

Dividing both sides by $2,$ we get

$x\le -\frac{5}{2}$

Given $x-3\le 0$

Add $-3$ on both sides, we get

$x-3+3\le 0+3$

$\Rightarrow x\le 3$

Then $x\le -\frac{5}{2}$and $x\le 3$

$\Rightarrow x\le -\frac{5}{2}$