Question

solve the inequality and graph the solution. 1 ≤ (v/3) - 1 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. -10 -8 -6 -4 -2 0 2 4 6 8 10

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( v \), we add 1 to both sides of the inequality \( 1 \leq \frac{v}{3}-1 \). This gives \( 1 + 1 \leq \frac{v}{3}-1 + 1 \), which simplifies to \( 2 \leq \frac{v}{3} \).

Step2: Multiply both sides by 3

To solve for \( v \), we multiply both sides of the inequality \( 2 \leq \frac{v}{3} \) by 3. This gives \( 2\times3 \leq \frac{v}{3}\times3 \), which simplifies to \( 6 \leq v \) or \( v \geq 6 \).

Answer:

The solution to the inequality is \( v \geq 6 \). To graph this, we plot a closed dot at 6 (since the inequality is "greater than or equal to") and draw a ray to the right of 6 on the number line.