Question

solve the inequality and graph the solution.
9 > \frac{z}{-4} + 10
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Subtract 10 from both sides

$$9 - 10>\frac{z}{-4}+10 - 10$$
$$-1>\frac{z}{-4}$$

Step2: Multiply both sides by -4 and reverse the inequality sign

$$-1\times(-4)<\frac{z}{-4}\times(-4)$$
$$4 < z$$
$$z>4$$

Answer:

The solution of the inequality is \(z > 4\). On the number - line, we plot an open circle at \(4\) (because \(4\) is not included in the solution) and draw an arrow to the right.