Question

solve the following inequality. 2(5y - 6)≥5(3y + 6)
select the correct choice below and fill in the answer box to complete your choice.
a. the solution set is {y|y > }
b. the solution set is {y|y ≥ }
c. the solution set is {y|y < }
d. the solution set is {y|y ≤ }

Explanation:

Step1: Expand both sides

$2(5y - 6)=10y-12$ and $5(3y + 6)=15y + 30$, so the inequality becomes $10y-12\geq15y + 30$.

Step2: Move y - terms to one side

Subtract $10y$ from both sides: $10y-10y - 12\geq15y-10y + 30$, which simplifies to $-12\geq5y + 30$.

Step3: Move constant terms to one side

Subtract 30 from both sides: $-12-30\geq5y+30 - 30$, getting $-42\geq5y$.

Step4: Solve for y

Divide both sides by 5: $y\leq-\frac{42}{5}=-8.4$.

Answer:

D. The solution set is $\{y|y\leq - 8.4\}$