Question

solve the inequality. then graph the solution set on a number line.
progress: 0/2
part 1 of 2
(a) solve 3(y + 2) + 3 ≥ 4(2y + 3) + 7 and simplify your answer as much as possible.

Explanation:

Step1: Expand both sides

Expand \(3(y + 2)+3\) to get \(3y + 6 + 3 = 3y + 9\). Expand \(4(2y + 3)+7\) to get \(8y + 12 + 7 = 8y + 19\). So the inequality becomes \(3y + 9 \geq 8y + 19\).

Step2: Move terms with y to one side

Subtract \(3y\) from both sides: \(9 \geq 5y + 19\). Then subtract 19 from both sides: \(9 - 19 \geq 5y\), which simplifies to \(-10 \geq 5y\).

Step3: Solve for y

Divide both sides by 5: \(\frac{-10}{5} \geq y\), so \(y \leq -2\).

Answer:

\(y \leq -2\)