Solve 3/2(2+5y)-y=1

$$\frac { 3 } { 2 } ( 2 + 5 y ) - y = 1$$

Solve for y

$$y=-\frac{4}{13}\approx -0.307692308$$

Steps for Solving Linear Equation

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

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

Cancel out 2 and 2.

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

Express \frac{3}{2}\times 5 as a single fraction.

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

Multiply 3 and 5 to get 15.

$$3+\frac{15}{2}y-y=1$$

Combine \frac{15}{2}y and -y to get \frac{13}{2}y.

$$3+\frac{13}{2}y=1$$

Subtract 3 from both sides.

$$\frac{13}{2}y=1-3$$

Subtract 3 from 1 to get -2.

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

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

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

Express -2\times \frac{2}{13} as a single fraction.

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

Multiply -2 and 2 to get -4.

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

Fraction \frac{-4}{13} can be rewritten as -\frac{4}{13} by extracting the negative sign.

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