Question

solve the compound inequality.
-3w < 0 or 2w - 2 ≥ -12
graph the solution on the number line.
if there is no solution, click on
o solution\.

Explanation:

Step1: Solve the first inequality

Divide both sides of $-3w < 0$ by $- 3$. When dividing an inequality by a negative number, the inequality sign flips. So we get $w>0$.

Step2: Solve the second inequality

Add 2 to both sides of $2w - 2\geq - 12$, we have $2w\geq - 12 + 2$, which simplifies to $2w\geq - 10$. Then divide both sides by 2, we get $w\geq - 5$.

Step3: Analyze the 'or' condition

The solution of the compound - inequality $-3w < 0$ or $2w - 2\geq - 12$ is the union of the solutions of the two individual inequalities. Since $w>0$ or $w\geq - 5$, the overall solution is $w\geq - 5$.

Answer:

The solution is $w\geq - 5$. To graph it on the number - line, we use a closed circle at $w=-5$ (because $w = - 5$ is included in the solution set) and draw an arrow to the right.