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 :

Certainly! Let's determine the steps you can use to isolate and solve for the variable \( x \) in the equation:

[tex]\[ \frac{6}{7} x + \frac{1}{2} - \frac{7}{8} = 0 \][/tex]

Here are the steps, detailed step-by-step:

1. Subtract \(\frac{1}{2}\) from both sides of the equation:
To isolate the term involving \( x \), we first subtract \(\frac{1}{2}\) from both sides:

[tex]\[ \frac{6}{7} x + \frac{1}{2} - \frac{1}{2} - \frac{7}{8} = 0 - \frac{1}{2} \][/tex]

Simplifies to:

[tex]\[ \frac{6}{7} x - \frac{7}{8} = -\frac{1}{2} \][/tex]

2. Use the Least Common Denominator (LCD) of 2 to combine like terms:
Notice that we have fractions with different denominators. To combine these terms, we need to express them with a common denominator. The LCD of \(\frac{1}{2}\) and \(\frac{7}{8}\) is 8. Expressing all terms with the common denominator, we can rewrite:

[tex]\[ \frac{6}{7} x = \frac{-4}{8} + \frac{7}{8} \][/tex]

Simplifies to:

[tex]\[ \frac{6}{7} x = \frac{3}{8} \][/tex]

3. Divide both sides by \(\frac{6}{7}\):
To isolate \( x \), we divide both sides by \(\frac{6}{7}\):

[tex]\[ x = \frac{\frac{3}{8}}{\frac{6}{7}} \][/tex]

4. Multiply both sides by \(\frac{7}{6}\):
Simplifying the division of fractions by multiplying by the reciprocal:

[tex]\[ x = \frac{3}{8} \times \frac{7}{6} = x \][/tex]

So, to solve the given equation for \( x \), you can use the following steps:

- Subtract \(\frac{1}{2}\) from both sides of the equation.
- Use the LCD of 2 to combine like terms.
- Divide both sides by \(\frac{6}{7}\)
- Multiply both sides by \(\frac{7}{6}\).

These steps will allow you to isolate [tex]\( x \)[/tex] and solve for its value.