Solve -8/3=1/2y-7/5

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

Solve for y

$$y = -\frac{38}{15} = -2\frac{8}{15} \approx -2.533333333$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Add \frac{7}{5} to both sides.

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

Least common multiple of 3 and 5 is 15. Convert -\frac{8}{3} and \frac{7}{5} to fractions with denominator 15.

$$\frac{1}{2}y=-\frac{40}{15}+\frac{21}{15}$$

Since -\frac{40}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}y=\frac{-40+21}{15}$$

Add -40 and 21 to get -19.

$$\frac{1}{2}y=-\frac{19}{15}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$y=-\frac{19}{15}\times 2$$

Express -\frac{19}{15}\times 2 as a single fraction.

$$y=\frac{-19\times 2}{15}$$

Multiply -19 and 2 to get -38.

$$y=\frac{-38}{15}$$

Fraction \frac{-38}{15} can be rewritten as -\frac{38}{15} by extracting the negative sign.

$$y=-\frac{38}{15}$$