Question

solve the equation.
\\(\frac{a}{4} - \frac{5}{6} = -\frac{1}{2}\\)
\\(a = \square\\)

Explanation:

Step1: Add $\frac{5}{6}$ to both sides

To isolate the term with \(a\), we add \(\frac{5}{6}\) to both sides of the equation \(\frac{a}{4}-\frac{5}{6}=-\frac{1}{2}\). This gives us \(\frac{a}{4}=-\frac{1}{2}+\frac{5}{6}\).

Step2: Find a common denominator and add

The common denominator of 2 and 6 is 6. So we rewrite \(-\frac{1}{2}\) as \(-\frac{3}{6}\). Then we add: \(-\frac{3}{6}+\frac{5}{6}=\frac{-3 + 5}{6}=\frac{2}{6}=\frac{1}{3}\). Now our equation is \(\frac{a}{4}=\frac{1}{3}\).

Step3: Multiply both sides by 4

To solve for \(a\), we multiply both sides of the equation \(\frac{a}{4}=\frac{1}{3}\) by 4. This gives us \(a=\frac{1}{3}\times4=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\)