Question

solve the inequality and graph the solution.
-2v + 8 > 2
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.
(there is a number line from -5 to 5 with a submit button on the left side and options learn with an example or watch a video on the right side.)

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( v \), we subtract 8 from both sides of the inequality \( -2v + 8>2 \). This gives us \( -2v + 8 - 8>2 - 8 \), which simplifies to \( -2v>-6 \).

Step2: Divide by -2 (reverse inequality)

When dividing both sides of an inequality by a negative number, we must reverse the inequality sign. Dividing both sides of \( -2v>-6 \) by -2, we get \( \frac{-2v}{-2}<\frac{-6}{-2} \), which simplifies to \( v < 3 \).

Answer:

The solution to the inequality is \( v < 3 \). To graph this, we draw an open circle at \( v = 3 \) (since the inequality is strict, \( v
eq3 \)) and shade the region to the left of 3 on the number line.