Question

solve the compound inequality. 2v - 5 ≥ - 3 or - 3v < - 15 graph the solution on the number line. if there is no solution, click on
o solution\.

Explanation:

Step1: Solve the first inequality

Add 5 to both sides of $2v - 5\geq - 3$: $2v-5 + 5\geq - 3+5$, which simplifies to $2v\geq2$. Then divide both sides by 2: $\frac{2v}{2}\geq\frac{2}{2}$, so $v\geq1$.

Step2: Solve the second inequality

Divide both sides of $-3v\lt - 15$ by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $\frac{-3v}{-3}>\frac{-15}{-3}$, which gives $v > 5$.

Step3: Analyze the 'or' compound - inequality

The solution of the compound - inequality $2v - 5\geq - 3$ or $-3v\lt - 15$ is the union of the solutions of the two individual inequalities. Since $v\geq1$ or $v > 5$, the overall solution is $v\geq1$.

Answer:

The solution is $v\geq1$. On the number - line, we use a closed circle at 1 (because 1 is included in the solution set, due to $\geq$) and draw an arrow to the right to represent all values greater than or equal to 1.