Question

solve for w and graph the solution.
\frac{3w + 10}{2}<8 or \frac{3w - 2}{2}>8
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Multiply both sides of $\frac{3w + 10}{2}<8$ by 2: $3w + 10<16$. Then subtract 10 from both sides: $3w<16 - 10$, so $3w<6$. Divide both sides by 3: $w < 2$.

Step2: Solve the second inequality

Multiply both sides of $\frac{3w - 2}{2}>8$ by 2: $3w-2 > 16$. Add 2 to both sides: $3w>16 + 2$, so $3w>18$. Divide both sides by 3: $w>6$.

Answer:

The solution is $w < 2$ or $w>6$. On the number - line, an open circle at 2 with an arrow pointing to the left and an open circle at 6 with an arrow pointing to the right.