Question

solve the inequality and graph the solution. -10(v + 3) ≤ 10 plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it. submit

Explanation:

Step1: Expand the left - hand side

$$-10(v + 3)=-10v-30$$
The inequality becomes $-10v - 30\leq10$.

Step2: Add 30 to both sides

$$-10v-30 + 30\leq10 + 30$$
$$-10v\leq40$$

Step3: Divide both sides by - 10 (and reverse the inequality sign)

When dividing an inequality by a negative number, the inequality sign flips.
$$\frac{-10v}{-10}\geq\frac{40}{-10}$$
$$v\geq - 4$$

Answer:

The solution of the inequality is $v\geq - 4$. On the number line, we plot a closed circle at $-4$ (because the inequality includes equality, $\leq$ was transformed to $\geq$ after dividing by a negative, but the original inequality $-10(v + 3)\leq10$ when solved gives $v\geq - 4$ and the "=" part still holds) and draw a ray to the right.