Question

Which steps can be used to solve StartFraction 6 Over 7 EndFraction x + one-half = StartFraction 7 Over 8 EndFraction for x? Check all that apply.
Divide both sides of the equation by StartFraction 7 Over 8 EndFraction.
Subtract One-half from both sides of the equation.
Use the LCD of 2 to combine like terms.
Divide both sides by StartFraction 6 Over 7 EndFraction.
Multiply both sides by StartFraction 7 Over 8 EndFraction.

Answer 1

To solve the equation \(\frac{6}{7}x + \frac{1}{2} = \frac{7}{8}\) for \(x\), the following steps can be used:

1. **Subtract \(\frac{1}{2}\) from both sides of the equation.**
- This will isolate the term with \(x\) on one side.

2. **Use the LCD of 2 to combine like terms (if simplifying the left side after subtraction).**
- This would help when combining \(\frac{1}{2}\) and other fractions that appear.

3. **Divide both sides by \(\frac{6}{7}\) or equivalently multiply both sides by \(\frac{7}{6}\).**
- This is essential to isolate \(x\) after rearranging the equation.

So the applicable steps are:
- **Subtract \(\frac{1}{2}\) from both sides of the equation.**
- **Use the LCD of 2 to combine like terms.**
- **Divide both sides by \(\frac{6}{7}\)** (or equivalently multiply by its reciprocal).

The steps that do NOT apply:
- **Divide both sides by \(\frac{7}{8}\)** is not useful in this context since we need to deal with \(\frac{6}{7}\).
- **Multiply both sides by \(\frac{7}{8}\)** is also irrelevant for isolating \(x\).

Therefore, the applicable steps are the first, second, and fourth options listed above.