Question

solve the inequality and graph the solution.
13 - v < 11
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 13 from both sides

To isolate the term with \( v \), we subtract 13 from both sides of the inequality \( 13 - v < 11 \).
\[
13 - v - 13 < 11 - 13
\]
Simplifying both sides gives:
\[
-v < -2
\]

Step2: Multiply both sides by -1 (reverse inequality)

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

Answer:

The solution to the inequality \( 13 - v < 11 \) is \( v > 2 \). To graph this, we place an open circle at \( 2 \) (since the inequality is strict, \( v
eq 2 \)) and draw an arrow to the right to represent all values greater than \( 2 \).