Solve 1/2(x+40)=-12/3(x-20)

$$\frac { 1 } { 2 } ( x + 40 ) = \frac { - 12 } { 3 } ( x - 20 )$$

Solve for x

$$x = \frac{40}{3} = 13\frac{1}{3} \approx 13.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+40.

$$\frac{1}{2}x+\frac{1}{2}\times 40=\frac{-12}{3}\left(x-20\right)$$

Multiply \frac{1}{2} and 40 to get \frac{40}{2}.

$$\frac{1}{2}x+\frac{40}{2}=\frac{-12}{3}\left(x-20\right)$$

Divide 40 by 2 to get 20.

$$\frac{1}{2}x+20=\frac{-12}{3}\left(x-20\right)$$

Divide -12 by 3 to get -4.

$$\frac{1}{2}x+20=-4\left(x-20\right)$$

Use the distributive property to multiply -4 by x-20.

$$\frac{1}{2}x+20=-4x+80$$

Add 4x to both sides.

$$\frac{1}{2}x+20+4x=80$$

Combine \frac{1}{2}x and 4x to get \frac{9}{2}x.

$$\frac{9}{2}x+20=80$$

Subtract 20 from both sides.

$$\frac{9}{2}x=80-20$$

Subtract 20 from 80 to get 60.

$$\frac{9}{2}x=60$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$x=60\times \frac{2}{9}$$

Express 60\times \frac{2}{9} as a single fraction.

$$x=\frac{60\times 2}{9}$$

Multiply 60 and 2 to get 120.

$$x=\frac{120}{9}$$

Reduce the fraction \frac{120}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{40}{3}$$