Question

solve the inequality and graph the solution.
4z + 9 > 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.

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \( z \), we subtract 9 from both sides of the inequality \( 4z + 9 > 1 \). This gives us \( 4z + 9 - 9 > 1 - 9 \), which simplifies to \( 4z > -8 \).

Step2: Divide both sides by 4

To solve for \( z \), we divide both sides of the inequality \( 4z > -8 \) by 4. This gives us \( \frac{4z}{4} > \frac{-8}{4} \), which simplifies to \( z > -2 \).

Answer:

The solution to the inequality \( 4z + 9 > 1 \) is \( z > -2 \). For the graph, we use an open circle at \( -2 \) (since the inequality is strict, \( > \), not \( \geq \)) and draw a ray to the right of \( -2 \) on the number line.