Question

Which of the following is the solution statement for the inequality shown below?
$-5<1-3x<10$

• A. $-5<x<10$
• B. $-3<x$
• C. $-3<x<2$
• D. $-2<x<3$

Answer 1

Answer: (C)

$-3<x<2$

Given, $-5<1-3x<10$

Subtracting $1$ from all, we get

$-5-1<1-3x-1<10-1$

$-6<-3x<9$

Dividing by $-3$, we get

$\frac{-6}{-3}>\frac{-3x}{-3}>\frac{9}{-3}$

Symbol changes from greater to lesser as we are dividing by negative number.

$2>x>-3$

Hence, option $C$ is correct.