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.
