Question

solve the inequality and graph the solution.
9 + 4r > 1
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 \( 9 + 4r > 1 \). This gives us \( 4r > 1 - 9 \), which simplifies to \( 4r > -8 \).

Step2: Divide by 4

Next, we divide both sides of the inequality \( 4r > -8 \) by 4 to solve for \( r \). This results in \( r > \frac{-8}{4} \), so \( r > -2 \).

To graph the solution:

• The endpoint is at \( r = -2 \). Since the inequality is \( > \) (not \( \geq \)), we use an open circle at \( -2 \).
• Then, we draw a ray to the right of \( -2 \) to represent all values of \( r \) greater than \( -2 \).

Answer:

The solution to the inequality \( 9 + 4r > 1 \) is \( r > -2 \). For the graph, place an open circle at \( -2 \) on the number line and draw a ray pointing to the right (towards positive infinity).