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

To graph this solution:

• The endpoint is at \( v = 2 \). Since the inequality is \( v < 2 \) (not \( v \leq 2 \)), we use an open circle at \( 2 \) to indicate that 2 is not included in the solution.
• Then, we draw a ray to the left of \( 2 \) (towards negative infinity) to represent all values of \( v \) that are less than 2.

Answer:

The solution to the inequality \( 4 - v > 2 \) is \( v < 2 \). The graph has an open circle at \( 2 \) and a ray extending to the left from \( 2 \).