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Which steps can be used to solve [tex]\frac{6}{7} x+\frac{1}{2}=\frac{7}{8}[/tex] for [tex]x[/tex]? Check all that apply.

A. Divide both sides of the equation by [tex]\frac{7}{8}[/tex].
B. Subtract [tex]\frac{1}{2}[/tex] from both sides of the equation.
C. Use the LCD of 2 to combine like terms.
D. Divide both sides by [tex]\frac{6}{7}[/tex].
E. Multiply both sides by [tex]\frac{7}{6}[/tex].



Answer :

GinnyAnswer
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].

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