Question

solve the inequality and graph the solution. 3(z + 29) - 12 < 69. 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: Expand the left - hand side

$3(z + 29)-12=3z+87 - 12=3z + 75$

Step2: Solve the inequality

$3z+75\lt69$
Subtract 75 from both sides:
$3z\lt69 - 75$
$3z\lt - 6$
Divide both sides by 3:
$z\lt - 2$

Answer:

The solution of the inequality is $z\lt - 2$. On the number - line, we use an open circle at $z=-2$ (since $z$ is strictly less than - 2) and draw a ray to the left of $z = - 2$.