Question

solve the following compound inequality.-6x+7<55 AND 5x-4≤16OA. x<-8 AND x < 4OB. -9< x≤4OC. -8 < x≤4OD. x≤4

Answer 1

The given compound inequality is:

`-6x+7\lt55\text{ and }5x-4\leq16`

Solve the first inequality:

`\begin{gathered} -6x+7<55 \\ -6x<55-7 \\ -6x<48 \\ \text{ Divide both sides by }-6\text{ and reverse the inequality sign:} \\ -(6x)/(-6)\gt(48)/(-6) \\ x\gt-8 \end{gathered}`

Solve the second inequality:

`\begin{gathered} 5x-4\leq16 \\ \text{ Add }4\text{ to both sides of the inequality:} \\ 5x-4+4\leq16+4 \\ 5x\leq20 \\ (5x)/(5)\leq(20)/(5) \\ x\leq4 \end{gathered}`

Therefore, the correct answer is choice C:

-8 < x ≤ 4