Question

solve the linear inequality for y. write your answer in inequality notation. 2 ≥ 6y + 8

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( y \), we subtract 8 from both sides of the inequality \( 2 \geq 6y + 8 \). This gives us \( 2 - 8 \geq 6y + 8 - 8 \), which simplifies to \( -6 \geq 6y \).

Step2: Divide both sides by 6

Next, we divide both sides of the inequality \( -6 \geq 6y \) by 6 to solve for \( y \). When we divide both sides by a positive number, the direction of the inequality sign remains the same. So we have \( \frac{-6}{6} \geq \frac{6y}{6} \), which simplifies to \( -1 \geq y \) or equivalently \( y \leq -1 \).

Answer:

\( y \leq -1 \)