Which value of x makes the equation 1.25(4x – 10) = 7.5 true

To solve the equation \( 1.25(4x - 10) = 7.5 \), follow these steps:

### Step 1: Distribute the 1.25 on the left-hand side
\[
1.25 \times 4x - 1.25 \times 10 = 7.5
\]
\[
5x - 12.5 = 7.5
\]

### Step 2: Add 12.5 to both sides to eliminate the constant on the left
\[
5x = 7.5 + 12.5
\]
\[
5x = 20
\]

### Step 3: Divide both sides by 5 to solve for \( x \)
\[
x = \frac{20}{5} = 4
\]

Thus, the value of \( x \) is \( \boxed{4} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the solution change if the constant on the right-hand side were different?
2. Can you solve a similar equation if the coefficient of \( x \) were a fraction instead of an integer?
3. What is the effect of changing the distributive constant (1.25 in this case) in such equations?
4. How do you solve equations involving more than one variable?
5. How would you check if your solution is correct by substituting the value back into the original equation?

**Tip**: Always check your solution by substituting the value of \( x \) back into the original equation to ensure it holds true.

Which value of x makes the equation 1.25(4x – 10) = 7.5 true?

Discover how to solve the linear equation 1.25(4x - 10) = 7.5 with a clear, step-by-step explanation. This problem highlights key algebraic concepts, including the distributive property and solving for x in linear equations. Suitable for students in Grades 6-8.

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