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

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;}`
`(2x+8)/(3)\ge2x-10`

To solve for the number;

`\begin{gathered} (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 \\ (-4x)/(-4)\leq(-38)/(-4) \\ x\leq9.5 \end{gathered}`

Final answer:

`x\leq9.5`