Question

Solve the system of inequalities: $-15<\frac{3(x-2)}{5}\le 0$.

• A. $-13<x\le 2$
• B. $-23<x\le 2$
• C. $-23<x\le 23$
• D. $-13\le x\le 23$

Answer 1

The correct option is B $-23<x\le 2$

$-15<\frac{3(x-2)}{5}\le 0$

If $-15<\frac{3(x-2)}{5}$

Multiply both sides by $5,$ we get

$-15\times 5<\frac{3(x-2)}{5}\times 5$

$\Rightarrow -75<3(x-2)$

$\Rightarrow -75<3x-6$

Add $6$ both sides, we get

$-75+6<3x-6+6$

$\Rightarrow -69<3x$

Dividing both sides by 3, we get

$-23<x$ ....... $\left(i\right)$

Also,

$\frac{3(x-2)}{5}\le 0$

$\Rightarrow 3(x-2)\le 0$

$\Rightarrow 3x-6\le 0$

$\Rightarrow 3x\le 6$

$\Rightarrow x\le 2$

Then $-23<x\le 2$