Question

solve for y and graph the solution.

1 ≥ \frac{-3y - 16}{2} ≥ -8

plot the endpoints. select an endpoint to change it from closed to open. select the m a segment, ray, or line to delete it.

Explanation:

Step1: Multiply all parts by 2

$$\begin{align*} 1\times2&\geq\frac{-3y - 16}{2}\times2\geq-8\times2\\ 2&\geq-3y - 16\geq-16 \end{align*}$$

Step2: Add 16 to all parts

$$\begin{align*} 2 + 16&\geq-3y-16 + 16\geq-16+16\\ 18&\geq-3y\geq0 \end{align*}$$

Step3: Divide all parts by -3 (reverse inequalities)

$$\begin{align*} \frac{18}{-3}&\leq\frac{-3y}{-3}\leq\frac{0}{-3}\\ -6&\leq y\leq0 \end{align*}$$

Answer:

The solution is \( -6\leq y\leq0 \). On the number - line, we plot a closed circle at \( y = - 6 \) and \( y = 0 \) and connect them with a segment.