Solve 15/4-3/2y-5y=7

$$\frac { 15 } { 4 } - \frac { 3 } { 2 } y - 5 y = 7$$

Solve for y

$$y=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Combine -\frac{3}{2}y and -5y to get -\frac{13}{2}y.

$$\frac{15}{4}-\frac{13}{2}y=7$$

Subtract \frac{15}{4} from both sides.

$$-\frac{13}{2}y=7-\frac{15}{4}$$

Convert 7 to fraction \frac{28}{4}.

$$-\frac{13}{2}y=\frac{28}{4}-\frac{15}{4}$$

Since \frac{28}{4} and \frac{15}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{2}y=\frac{28-15}{4}$$

Subtract 15 from 28 to get 13.

$$-\frac{13}{2}y=\frac{13}{4}$$

Multiply both sides by -\frac{2}{13}, the reciprocal of -\frac{13}{2}.

$$y=\frac{13}{4}\left(-\frac{2}{13}\right)$$

Multiply \frac{13}{4} times -\frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{13\left(-2\right)}{4\times 13}$$

Cancel out 13 in both numerator and denominator.

$$y=\frac{-2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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