Question

solve the inequality and graph the solution.
7 + 3z ≥ 1
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
submit

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( z \), we subtract 7 from both sides of the inequality \( 7 + 3z \geq 1 \).
\( 7 + 3z - 7 \geq 1 - 7 \)
Simplifying both sides, we get \( 3z \geq -6 \).

Step2: Divide both sides by 3

To solve for \( z \), we divide both sides of the inequality \( 3z \geq -6 \) by 3.
\( \frac{3z}{3} \geq \frac{-6}{3} \)
Simplifying, we find \( z \geq -2 \).

Answer:

The solution to the inequality \( 7 + 3z \geq 1 \) is \( z \geq -2 \). To graph this, we plot a closed dot at \( z = -2 \) (since the inequality is "greater than or equal to") and draw a ray to the right of \( -2 \) on the number line.