Question

solve for y.
$4 + \frac{7}{y} = \frac{5}{3}$
simplify your answer as much as possible.
$y = \square$

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( y \), we subtract 4 from both sides of the equation \( 4 + \frac{7}{y} = \frac{5}{3} \). This gives us \( \frac{7}{y} = \frac{5}{3} - 4 \). We convert 4 to a fraction with denominator 3: \( 4 = \frac{12}{3} \). So, \( \frac{7}{y} = \frac{5}{3} - \frac{12}{3} = \frac{5 - 12}{3} = \frac{-7}{3} \).

Step2: Solve for \( y \)

Now we have \( \frac{7}{y} = -\frac{7}{3} \). We can cross - multiply (or take the reciprocal of both sides after some manipulation). Cross - multiplying gives us \( 7\times3=-7\times y \), which simplifies to \( 21 = - 7y \). Then, divide both sides by -7: \( y=\frac{21}{-7}=-3 \).

Answer:

\( y = - 3 \)