Question

I'm having trouble with my math homework. Can you find the solution to the inequality 1.25x - 12.75 = 16.5 and show me the step-by-step process to solve it?

Answer 1

To solve the equation \( 1.25x - 12.75 = 16.5 \), we want to isolate \( x \). Here are the steps to do that:

1. **Add 12.75 to both sides of the equation** to eliminate the constant on the left side:
\[
1.25x - 12.75 + 12.75 = 16.5 + 12.75
\]
This simplifies to:
\[
1.25x = 29.25
\]

2. **Divide both sides by 1.25** to solve for \( x \):
\[
x = \frac{29.25}{1.25}
\]

3. **Perform the division**. To make it easier, convert 29.25 and 1.25 to fractions:
\[
29.25 = \frac{2925}{100}, \quad 1.25 = \frac{125}{100}
\]
So,
\[
x = \frac{\frac{2925}{100}}{\frac{125}{100}} = \frac{2925}{125}
\]

4. **Simplify \( \frac{2925}{125} \)**. Now, perform the division:
\[
2925 \div 125 = 23.4
\]
Thus,
\[
x = 23.4
\]

The solution to the equation \( 1.25x - 12.75 = 16.5 \) is:
\[
\boxed{23.4}
\]