Question

If $8<15mx-7<24$, where m is a positive constant, what is the possible range of values of -5mx.

• A. Any value greater than -5 or less than $-\frac{31}{5}$
• B. Any value greater than $-\frac{31}{5}$ and less than -5
• C. Any value greater than $-\frac{7}{3m}$ or less than $-\frac{31}{15m}$
• D. Any value greater than $-\frac{31}{15m}$ or less than $-\frac{7}{3m}$

Answer 1

The correct option is B Any value greater than $-\frac{31}{5}$ and less than -5

Lets examine the structure of inequality $8<15mx-7<24$

Add 7 on each side $8+7<15mx-7+7<24+7$
$15<15mx<31$

Divide by 3 on both side $\frac{15}{3}<\frac{15mx}{3}<\frac{31}{5}$
$5<5mx<\frac{31}{3}$

Multiply -1 on both sides (flip the sign )
$-5>-5mx>-\frac{31}{3}$
$-\frac{31}{3}<-5mx<-5$

Hence, the correct answer is option B.