Question

question 4 of 10, step 2 of 2
step 2 of 2: graph the solution set.
-2 ≤ -2(x - 2) < 2
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pressing the buttons will create an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed intervals, use the clear button. to indicate infinity or negative infinity, drag an open end point to the end of the number line.
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Explanation:

Step1: Solve left inequality

Start with $-2 \leq -2(z-2)$.
Divide by $-2$ (reverse inequality):
$1 \geq z-2$
Add 2 to both sides:
$z \leq 3$

Step2: Solve right inequality

Start with $-2(z-2) < 2$.
Divide by $-2$ (reverse inequality):
$z-2 > -1$
Add 2 to both sides:
$z > 1$

Step3: Combine inequalities

Combine the two results:
$1 < z \leq 3$

Step4: Graph setup

On the number line:

• Place an open circle at $z=1$ (since $z>1$, no equality)
• Place a closed circle at $z=3$ (since $z\leq3$, includes equality)
• Shade the region between 1 and 3.

Answer:

The solution set is $1 < z \leq 3$. To graph:

1. Draw an open endpoint at $1$, a closed endpoint at $3$.
2. Shade the interval between $1$ and $3$.