Question

solve for y.
\\(\displaystyle -\frac{7}{8} = \frac{1}{2}y - \frac{5}{3}\\)
simplify your answer as much as possible.
\\(\displaystyle y = \boxed{}\\)

Explanation:

Step1: Add $\frac{5}{3}$ to both sides

To isolate the term with \( y \), we add \(\frac{5}{3}\) to both sides of the equation \(-\frac{7}{8}=\frac{1}{2}y - \frac{5}{3}\).

$$ -\frac{7}{8}+\frac{5}{3}=\frac{1}{2}y - \frac{5}{3}+\frac{5}{3} $$

First, find a common denominator for \(-\frac{7}{8}\) and \(\frac{5}{3}\), which is \(24\).

$$ -\frac{7\times3}{8\times3}+\frac{5\times8}{3\times8}=-\frac{21}{24}+\frac{40}{24}=\frac{-21 + 40}{24}=\frac{19}{24} $$

So the equation becomes \(\frac{19}{24}=\frac{1}{2}y\).

Step2: Multiply both sides by 2

To solve for \( y \), we multiply both sides of the equation \(\frac{19}{24}=\frac{1}{2}y\) by \(2\).

$$ 2\times\frac{19}{24}=\frac{1}{2}y\times2 $$

Simplify the left side: \(\frac{38}{24}=\frac{19}{12}\). The right side simplifies to \(y\).

Answer:

\(y = \frac{19}{12}\)