Solve 1/2(8x-50)=2/3x

$$\frac { 1 } { 2 } ( 8 x - 50 ) = \frac { 2 } { 3 } x$$

Solve for x

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 8x-50.

$$\frac{1}{2}\times 8x+\frac{1}{2}\left(-50\right)=\frac{2}{3}x$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$\frac{8}{2}x+\frac{1}{2}\left(-50\right)=\frac{2}{3}x$$

Divide 8 by 2 to get 4.

$$4x+\frac{1}{2}\left(-50\right)=\frac{2}{3}x$$

Multiply \frac{1}{2} and -50 to get \frac{-50}{2}.

$$4x+\frac{-50}{2}=\frac{2}{3}x$$

Divide -50 by 2 to get -25.

$$4x-25=\frac{2}{3}x$$

Subtract \frac{2}{3}x from both sides.

$$4x-25-\frac{2}{3}x=0$$

Combine 4x and -\frac{2}{3}x to get \frac{10}{3}x.

$$\frac{10}{3}x-25=0$$

Add 25 to both sides. Anything plus zero gives itself.

$$\frac{10}{3}x=25$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}.

$$x=25\times \frac{3}{10}$$

Express 25\times \frac{3}{10} as a single fraction.

$$x=\frac{25\times 3}{10}$$

Multiply 25 and 3 to get 75.

$$x=\frac{75}{10}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{15}{2}$$