Question

solve the inequality and graph the solution.
9 + 2r < 5
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 9 from both sides

To isolate the term with \( r \), we subtract 9 from both sides of the inequality \( 9 + 2r < 5 \). This gives us \( 9 + 2r - 9 < 5 - 9 \), which simplifies to \( 2r < -4 \).

Step2: Divide by 2

Next, we divide both sides of the inequality \( 2r < -4 \) by 2 to solve for \( r \). So, \( \frac{2r}{2} < \frac{-4}{2} \), which simplifies to \( r < -2 \).

Answer:

The solution to the inequality \( 9 + 2r < 5 \) is \( r < -2 \). To graph this, we draw an open circle at \( r = -2 \) (since the inequality is strict, \( r
eq -2 \)) and shade the line to the left of \( -2 \) to represent all values of \( r \) less than \( -2 \).