To solve the equation \(\frac{6}{7} x + \frac{1}{2} = \frac{7}{8}\) for \(x\), we can follow the below steps:
1. Subtract \(\frac{1}{2}\) from both sides of the equation.
Starting with:
[tex]\[
\frac{6}{7} x + \frac{1}{2} = \frac{7}{8}
\][/tex]
Subtract \(\frac{1}{2}\) from both sides:
[tex]\[
\frac{6}{7} x + \frac{1}{2} - \frac{1}{2} = \frac{7}{8} - \frac{1}{2}
\][/tex]
Simplifying the right-hand side by getting a common denominator:
[tex]\[
\frac{6}{7} x = \frac{7}{8} - \frac{4}{8}
\][/tex]
[tex]\[
\frac{6}{7} x = \frac{3}{8}
\][/tex]
2. Multiply both sides by \(\frac{7}{6}\).
To isolate \(x\), multiply both sides by the reciprocal of \(\frac{6}{7}\):
[tex]\[
x = \frac{3}{8} \times \frac{7}{6}
\][/tex]
By performing the multiplication:
[tex]\[
x = \frac{3 \times 7}{8 \times 6} = \frac{21}{48} = \frac{7}{16} = 0.4375
\][/tex]
Therefore, the correct steps are:
- Subtract \(\frac{1}{2}\) from both sides of the equation.
- Multiply both sides by \(\frac{7}{6}\).
So, the solution for which steps can be used to solve the equation, given the options, is:
- Subtract \(\frac{1}{2}\) from both sides of the equation.
- Multiply both sides by [tex]\(\frac{7}{6}\)[/tex].
