Question

solve for v and graph the solution.
-18 ≤ 5v - 3 < 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.
←
-6 -5 -4 -3 -2 -1 0 1

Explanation:

Step1: Add 3 to all parts

To isolate the term with \( v \), we add 3 to each part of the compound inequality.
\( -18 + 3 \leq 5v - 3 + 3 < 7 + 3 \)
Simplifying each part: \( -15 \leq 5v < 10 \)

Step2: Divide all parts by 5

To solve for \( v \), we divide each part of the inequality by 5.
\( \frac{-15}{5} \leq \frac{5v}{5} < \frac{10}{5} \)
Simplifying each part: \( -3 \leq v < 2 \)

Answer:

The solution for \( v \) is \( -3 \leq v < 2 \). To graph this, we plot a closed circle at \( -3 \) (since the inequality is \( \leq \)) and an open circle at \( 2 \) (since the inequality is \( < \)), then draw a line segment connecting these two points on the number line.