Question

solve the inequality and graph the solution.
9 + 2y > 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 \( y \), we subtract 9 from both sides of the inequality \( 9 + 2y > 5 \). This gives us \( 9 + 2y - 9 > 5 - 9 \), which simplifies to \( 2y > -4 \).

Step2: Divide both sides by 2

To solve for \( y \), we divide both sides of the inequality \( 2y > -4 \) by 2. This gives us \( \frac{2y}{2} > \frac{-4}{2} \), which simplifies to \( y > -2 \).

To graph the solution:

• The endpoint is at \( y = -2 \). Since the inequality is \( y > -2 \) (not \( y \geq -2 \)), we use an open circle at \( -2 \) on the number line.
• Then, we draw a ray starting from the open circle at \( -2 \) and pointing to the right (towards positive infinity) to represent all values of \( y \) greater than \( -2 \).

Answer:

The solution to the inequality \( 9 + 2y > 5 \) is \( y > -2 \). On the number line, there is an open circle at \( -2 \) and a ray extending to the right from \( -2 \).