Correctly order the steps used to solve this equation

Question

5/8(x+1/2)=100

Answer 1

To solve the equation \(\frac{5}{8}(x + \frac{1}{2}) = 100\), we can follow these steps in the correct order:

1. Multiply both sides by the reciprocal of \(\frac{5}{8}\) to eliminate the fraction: \[ x + \frac{1}{2} = 100 \times \frac{8}{5} \]

2. Calculate \(100 \times \frac{8}{5}\): \[ 100 \times \frac{8}{5} = 160 \]

3. Rewrite the equation without the fraction: \[ x + \frac{1}{2} = 160 \]

4. Subtract \(\frac{1}{2}\) from both sides to isolate \(x\): \[ x = 160 - \frac{1}{2} \]

5. Convert \(160\) to a fraction to perform the subtraction: \[ 160 = \frac{320}{2} \]

6. Perform the subtraction: \[ x = \frac{320}{2} - \frac{1}{2} = \frac{319}{2} \]

7. Final answer: \[ x = 159.5 \]

So, the ordered steps are:

1. Multiply both sides by \(\frac{8}{5}\).
2. Calculate \(100 \times \frac{8}{5}\).
3. Rewrite the equation.
4. Subtract \(\frac{1}{2}\) from both sides.
5. Convert \(160\) to a fraction.
6. Perform the subtraction.
7. State the solution for \(x\).