Question

solve the inequality and graph the solution. 8 + 6z ≥ 20 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. -5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( z \), we subtract 8 from both sides of the inequality \( 8 + 6z \geq 20 \).

$$ 8 + 6z - 8 \geq 20 - 8 $$

Simplifying both sides, we get:

$$ 6z \geq 12 $$

Step2: Divide both sides by 6

To solve for \( z \), we divide both sides of the inequality \( 6z \geq 12 \) by 6.

$$ \frac{6z}{6} \geq \frac{12}{6} $$

Simplifying both sides, we get:

$$ z \geq 2 $$

To graph the solution:

• The endpoint is at \( z = 2 \). Since the inequality is \( \geq \), we use a closed dot at \( 2 \).
• Then we draw a ray starting at \( 2 \) (with the closed dot) and extending to the right (towards positive infinity) because \( z \) is greater than or equal to 2.

Answer:

The solution to the inequality is \( z \geq 2 \). For the graph, place a closed dot at \( 2 \) on the number line and draw a ray to the right from \( 2 \).