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To solve this question, we need to check which equations have a solution of \( x = 4.5 \). Let's evaluate each equation:

1. **\( 5x - 1.5 = 21 \)**

Substitute \( x = 4.5 \):
\[
5(4.5) - 1.5 = 22.5 - 1.5 = 21
\]
This is **true**.

2. **\( 2(x + 1) - 1 = 10 \)**

Substitute \( x = 4.5 \):
\[
2(4.5 + 1) - 1 = 2(5.5) - 1 = 11 - 1 = 10
\]
This is **true**.

3. **\( 2(x + 1) - 5 = 6 \)**

Substitute \( x = 4.5 \):
\[
2(4.5 + 1) - 5 = 2(5.5) - 5 = 11 - 5 = 6
\]
This is **true**.

4. **\( 3x + 0.75 - 5 = 10.75 \)**

Substitute \( x = 4.5 \):
\[
3(4.5) + 0.75 - 5 = 13.5 + 0.75 - 5 = 14.25 - 5 = 9.25
\]
This is **false**.

5. **\( 2(2x - 3) = 12 \)**

Substitute \( x = 4.5 \):
\[
2(2(4.5) - 3) = 2(9 - 3) = 2(6) = 12
\]
This is **true**.

### Correct Equations:
- \( 5x - 1.5 = 21 \)
- \( 2(x + 1) - 1 = 10 \)
- \( 2(x + 1) - 5 = 6 \)
- \( 2(2x - 3) = 12 \)

Would you like more details or have any questions?

Here are 5 questions related to this:
1. How do you verify the solution of an equation?
2. Can you solve similar equations with other values of \( x \)?
3. Why is it important to substitute values to check the solution?
4. How can you identify if an equation has no solution?
5. What happens when equations have more than one solution?

**Tip:** Always simplify the equation after substituting values to make the verification process easier.

Which equations have a solution of 4.5? Select all that apply.

Learn how to solve linear equations by substituting x = 4.5. This problem tests various algebraic expressions and checks which of them hold true for the given solution. Suitable for students in Grades 6-8.

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