Question

39. The quotient of twice a number plus 8 and 3 is greater than or equal totwice the number less 10.Which Inequality and solution accurately solves for the number?

Answer 1

SOLUTION

Given:

39. The quotient of twice a number plus 8 and 3 is greater than or equal to

twice the number less 10.

Which Inequality and solution accurately solves for the number?

$Let\text{ the number be x;}$$\frac{2x+8}{3}\ge2x-10$

To solve for the number;

$\begin{gathered} \frac{2x+8}{3}\ge2x-10 \\ \text{ multiply both sides by 3;} \\ 2x+8\ge6x-30 \\ subtract\text{ 6x from both sides;} \\ 2x-6x+8\ge6x-6x-30 \\ -4x+8\ge-30 \\ -4x\ge-38 \\ \frac{-4x}{-4}\leq\frac{-38}{-4} \\ x\leq9.5 \end{gathered}$

Final answer:

$x\leq9.5$