Question

solve the inequality and graph the solution.
4 - v > 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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( v \), we subtract 4 from both sides of the inequality \( 4 - v > 2 \). This gives us \( 4 - v - 4 > 2 - 4 \), which simplifies to \( -v > -2 \).

Step2: Multiply by -1 (reverse inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. Multiplying both sides of \( -v > -2 \) by -1 gives \( v < 2 \).

Answer:

The solution to the inequality \( 4 - v > 2 \) is \( v < 2 \). To graph this, we draw an open circle at \( 2 \) (since \( v \) is not equal to \( 2 \)) and shade the line to the left of \( 2 \) to represent all values of \( v \) less than \( 2 \).