Solve 3/2(y-5)+10=2y

$$\frac { 3 } { 2 } ( y - 5 ) + 10 = 2 y$$

Solve for y

$$y=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{2} by y-5.

$$\frac{3}{2}y+\frac{3}{2}\left(-5\right)+10=2y$$

Express \frac{3}{2}\left(-5\right) as a single fraction.

$$\frac{3}{2}y+\frac{3\left(-5\right)}{2}+10=2y$$

Multiply 3 and -5 to get -15.

$$\frac{3}{2}y+\frac{-15}{2}+10=2y$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{3}{2}y-\frac{15}{2}+10=2y$$

Convert 10 to fraction \frac{20}{2}.

$$\frac{3}{2}y-\frac{15}{2}+\frac{20}{2}=2y$$

Since -\frac{15}{2} and \frac{20}{2} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}y+\frac{-15+20}{2}=2y$$

Add -15 and 20 to get 5.

$$\frac{3}{2}y+\frac{5}{2}=2y$$

Subtract 2y from both sides.

$$\frac{3}{2}y+\frac{5}{2}-2y=0$$

Combine \frac{3}{2}y and -2y to get -\frac{1}{2}y.

$$-\frac{1}{2}y+\frac{5}{2}=0$$

Subtract \frac{5}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{2}y=-\frac{5}{2}$$

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

$$y=-\frac{5}{2}\left(-2\right)$$

Express -\frac{5}{2}\left(-2\right) as a single fraction.

$$y=\frac{-5\left(-2\right)}{2}$$

Multiply -5 and -2 to get 10.

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

Divide 10 by 2 to get 5.

$$y=5$$