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We are given the inequality:

\[
12 + z \geq 18
\]

To solve for \( z \), we subtract 12 from both sides:

\[
z \geq 18 - 12
\]
\[
z \geq 6
\]

Now, let's check which values from the given options satisfy this inequality. The options are:

- \( z = 1 \)
- \( z = 6 \)
- \( z = 3 \)
- \( z = 4 \)

Only \( z = 6 \) satisfies \( z \geq 6 \).

Thus, the solution is \( z = 6 \).

Would you like more details on this problem? Here are five related questions to explore:

1. What happens if the inequality is \( 12 + z > 18 \)?
2. How would the solution change if it was \( 12 + z \leq 18 \)?
3. What is the difference between a strict inequality and a non-strict inequality?
4. Can you graph the inequality \( z \geq 6 \)?
5. How can inequalities be represented on a number line?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number in inequalities.

Which of the following is a solution to the inequality below?

12 + z ≥ 18

z = 1, z = 6, z = 3, z = 4

Learn how to solve the inequality 12 + z ≥ 18 and determine which of the given values satisfies the inequality. This problem involves basic algebra and inequality properties, suitable for students in Grades 6-8.

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