https://file.aiquickdraw.com/mathbot/file/1727790735131ga83do8k.jpg

The inequality given in the image is:

\[
2h \geq 10
\]

### Step 1: Solving for \( h \)

To isolate \( h \), divide both sides of the inequality by 2:

\[
h \geq \frac{10}{2}
\]

\[
h \geq 5
\]

This means that \( h \) must be greater than or equal to 5.

### Step 2: Selecting the values that make the inequality true

Now, let's check which values satisfy \( h \geq 5 \) from the given options:

- \(-5\) does not satisfy \( h \geq 5 \)
- \( 0 \) does not satisfy \( h \geq 5 \)
- \( 2 \) does not satisfy \( h \geq 5 \)
- \( 4 \) does not satisfy \( h \geq 5 \)
- \( 5 \) satisfies \( h \geq 5 \)
- \( 6 \) satisfies \( h \geq 5 \)
- \( 8 \) satisfies \( h \geq 5 \)
- \( 10 \) satisfies \( h \geq 5 \)
- \( 15 \) satisfies \( h \geq 5 \)

Thus, the correct values are:

\[ 5, 6, 8, 10, 15 \]

### Step 3: Writing an equivalent inequality

We already solved for \( h \) in the equivalent inequality, which is:

\[
h \geq 5
\]

Would you like further clarification or more details?

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Here are 5 related questions to further your understanding:

1. What happens if the inequality was \( 2h \leq 10 \)?
2. How do you solve inequalities that involve negative coefficients?
3. Can you graph the inequality \( h \geq 5 \) on a number line?
4. What would change if the inequality was a strict inequality \( 2h > 10 \)?
5. How do you solve multi-step inequalities involving both addition and multiplication?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.

Select the values that make the inequality 2h ≥ 10 true. Then write an equivalent inequality in terms of h.

Learn how to solve the inequality 2h ≥ 10 and identify which values satisfy the condition. Understand the key steps in solving algebraic inequalities and writing equivalent inequalities. Suitable for students in Grades 6-8.

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