Solve 2y-9/10+3/2=y

$$\frac { 2 y - 9 } { 10 } + \frac { 3 } { 2 } = y$$

Solve for y

$$y=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2 is 10. Multiply \frac{3}{2} times \frac{5}{5}.

$$\frac{2y-9}{10}+\frac{3\times 5}{10}=y$$

Since \frac{2y-9}{10} and \frac{3\times 5}{10} have the same denominator, add them by adding their numerators.

$$\frac{2y-9+3\times 5}{10}=y$$

Do the multiplications in 2y-9+3\times 5.

$$\frac{2y-9+15}{10}=y$$

Combine like terms in 2y-9+15.

$$\frac{2y+6}{10}=y$$

Divide each term of 2y+6 by 10 to get \frac{1}{5}y+\frac{3}{5}.

$$\frac{1}{5}y+\frac{3}{5}=y$$

Subtract y from both sides.

$$\frac{1}{5}y+\frac{3}{5}-y=0$$

Combine \frac{1}{5}y and -y to get -\frac{4}{5}y.

$$-\frac{4}{5}y+\frac{3}{5}=0$$

Subtract \frac{3}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{4}{5}y=-\frac{3}{5}$$

Multiply both sides by -\frac{5}{4}, the reciprocal of -\frac{4}{5}.

$$y=-\frac{3}{5}\left(-\frac{5}{4}\right)$$

Multiply -\frac{3}{5} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-3\left(-5\right)}{5\times 4}$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{5\times 4}.

$$y=\frac{15}{20}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$y=\frac{3}{4}$$