Question

If 9<15mx-8<279<15mx−8<279, is less than, 15, m, x, minus, 8, is less than, 27, where mmm is a positive constant, what is the possible range of values of \dfrac{8}{3}-5mx 3 8 ​ −5mxstart fraction, 8, divided by, 3, end fraction, minus, 5, m, x?

Answer 1

Answer:

The range of $\frac{8}{3}-5mx$ is (-9,-3).

Step-by-step explanation:

The given compound inequality is

$9<15mx-8<27$

We need to find the range of values of  $\frac{8}{3}-5mx$.

Let $y=\frac{8}{3}-5mx$

Divide each side of the given compound inequality by 3.

$\frac{9}{3}<\frac{15mx-8}{3}<\frac{27}{3}$

$3<\frac{15mx}{3}-\frac{8}{3}<9$

$3<5mx-\frac{8}{3}<9$

Multiply each side by -1.

If we multiply an inequality by a negative number, then the sign of inequality is changed.

$3(-1)>(5mx-\frac{8}{3})(-1)>9(-1)$      

$-3>-5mx+\frac{8}{3}>-9$

$-3>\frac{8}{3}-5mx>-9$

$-3>y>-9$

Therefore the range of $\frac{8}{3}-5mx$ is (-9,-3).