Question

solve for v and graph the solution. v - 1 - 12v ≥ 10 or 7v + 19 < 9v + 7 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

Combine like - terms in $v - 1-12v\geq10$.
$v-12v - 1\geq10$, so $- 11v-1\geq10$.
Add 1 to both sides: $-11v\geq10 + 1$, i.e., $-11v\geq11$.
Divide both sides by - 11 and reverse the inequality sign: $v\leq - 1$.

Step2: Solve the second inequality

Subtract 7v from both sides of $7v + 19<9v+7$:
$19<9v - 7v+7$, so $19<2v + 7$.
Subtract 7 from both sides: $19 - 7<2v$, i.e., $12<2v$.
Divide both sides by 2: $v>6$.

Answer:

The solution of the compound inequality is $v\leq - 1$ or $v>6$. On the number - line, there is a closed circle at $v=-1$ (for $v\leq - 1$) and an open circle at $v = 6$ (for $v>6$). The shaded regions are to the left of $v=-1$ and to the right of $v = 6$.