Question

solve the inequality and graph the solutio
-3 - z ≥ 3
to draw a ray, plot an endpoint and selec
closed to open. select the middle of the ra

Explanation:

Step1: Add 3 to both sides

To isolate the term with \( z \), we add 3 to both sides of the inequality \(-3 - z \geq 3\).
\[
-3 - z + 3 \geq 3 + 3
\]
Simplifying both sides, we get:
\[
-z \geq 6
\]

Step2: Multiply both sides by -1 (and reverse the inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \(-z \geq 6\) by -1.
\[
(-1)\times(-z) \leq (-1)\times6
\]
Simplifying both sides, we obtain:
\[
z \leq -6
\]

Answer:

The solution to the inequality is \( z \leq -6 \). To graph this, plot a closed dot at \(-6\) (since the inequality is "less than or equal to") and draw a ray to the left (towards negative infinity) from \(-6\).