Question

solve for y.
$-\frac{7}{3} = \frac{1}{3}y - \frac{3}{7}$
simplify your answer as much as possible.

Explanation:

Step1: Add $\frac{3}{7}$ to both sides

To isolate the term with \( y \), we add \( \frac{3}{7} \) to both sides of the equation.

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

First, calculate the left - hand side: find a common denominator for \( -\frac{7}{3} \) and \( \frac{3}{7} \), which is \( 21 \).

$$ -\frac{7\times7}{3\times7}+\frac{3\times3}{7\times3}=-\frac{49}{21}+\frac{9}{21}=\frac{- 49 + 9}{21}=\frac{-40}{21} $$

The right - hand side simplifies to \( \frac{1}{3}y \) since \( -\frac{3}{7}+\frac{3}{7}=0 \). So now we have \( \frac{-40}{21}=\frac{1}{3}y \).

Step2: Multiply both sides by 3

To solve for \( y \), we multiply both sides of the equation \( \frac{-40}{21}=\frac{1}{3}y \) by \( 3 \).

$$ 3\times\frac{-40}{21}=\frac{1}{3}y\times3 $$

Simplify the left - hand side: \( 3\times\frac{-40}{21}=\frac{-120}{21}=\frac{-40}{7} \) (dividing numerator and denominator by 3). The right - hand side simplifies to \( y \) since \( \frac{1}{3}\times3 = 1 \).

Answer:

\( y=-\frac{40}{7} \)