Question

Which of the following option represent the inequalities $-3\le 1-2x<7$ and $-5<\frac{4-3x}{4}<7$ on the number line?

• A.
• B.
• C.
• D. No Solution

Answer 1

The correct option is C

$-3\le 1-2x<7$
$\Rightarrow -4\le -2x<6$
$\Rightarrow -2\le -x<3$
$\Rightarrow -3<x\le 2...\left(1\right)$


Now, $-5<\frac{4-3x}{4}<7$
$\Rightarrow -20<4-3x<28$
$\Rightarrow -24<-3x<24$
$\Rightarrow -8<-x<8$
$\Rightarrow -8<x<8...\left(2\right)$


From $\left(1\right)$ and $\left(2\right)$


Hence, The common solution is