Solve 4(2y+3)=8(1-y)-5(y-2)

$$4 ( 2 y + 3 ) = 8 ( 1 - y ) - 5 ( y - 2 )$$

Solve for y

$$y=\frac{2}{7}\approx 0.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 2y+3.

$$8y+12=8\left(1-y\right)-5\left(y-2\right)$$

Use the distributive property to multiply 8 by 1-y.

$$8y+12=8-8y-5\left(y-2\right)$$

Use the distributive property to multiply -5 by y-2.

$$8y+12=8-8y-5y+10$$

Combine -8y and -5y to get -13y.

$$8y+12=8-13y+10$$

Add 8 and 10 to get 18.

$$8y+12=18-13y$$

Add 13y to both sides.

$$8y+12+13y=18$$

Combine 8y and 13y to get 21y.

$$21y+12=18$$

Subtract 12 from both sides.

$$21y=18-12$$

Subtract 12 from 18 to get 6.

$$21y=6$$

Divide both sides by 21.

$$y=\frac{6}{21}$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$y=\frac{2}{7}$$