Question

solve for ( y ) and graph the solution.

( 17 geq \frac{10 y - 29}{3} geq - 23 )

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

Explanation:

Step1: Multiply all parts by 3

$$\begin{align*} 17\times3&\geq\frac{10g - 29}{3}\times3\geq- 23\times3\\ 51&\geq10g-29\geq - 69 \end{align*}$$

Step2: Add 29 to all parts

$$\begin{align*} 51 + 29&\geq10g-29 + 29\geq-69 + 29\\ 80&\geq10g\geq - 40 \end{align*}$$

Step3: Divide all parts by 10

$$\begin{align*} \frac{80}{10}&\geq\frac{10g}{10}\geq\frac{-40}{10}\\ 8&\geq g\geq - 4 \end{align*}$$

Answer:

The solution is $-4\leq g\leq8$. On the number - line, we plot a closed circle at $g = - 4$ (since the inequality includes equality for $g\geq - 4$) and a closed circle at $g = 8$ (since the inequality includes equality for $g\leq8$) and connect them with a line segment.