Question

solve the following inequality.
-\frac{9}{8}x\geq -\frac{1}{16}
select the correct choice below and fill in the answer box to complete your choice.
a. the solution set is {x|x < }.
b. the solution set is {x|x\geq }.
c. the solution set is {x|x > }.
d. the solution set is {x|x\leq }.

Explanation:

Step1: Multiply both sides by -8/9

When multiplying an inequality by a negative number, the direction of the inequality sign changes. So we have $x\leq-\frac{1}{16}\times(-\frac{8}{9})$.

Step2: Calculate the right - hand side value

$-\frac{1}{16}\times(-\frac{8}{9})=\frac{1\times8}{16\times9}=\frac{1}{18}$.

Answer:

D. The solution set is $\{x|x\leq\frac{1}{18}\}$