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 \(-6\).