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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.

1 answer

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.