Solve 1/5(x+20)=-x+14+4/5x

$$\frac { 1 } { 5 } ( x + 20 ) = - x + 14 + \frac { 4 } { 5 } x$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by x+20.

$$\frac{1}{5}x+\frac{1}{5}\times 20=-x+14+\frac{4}{5}x$$

Multiply \frac{1}{5} and 20 to get \frac{20}{5}.

$$\frac{1}{5}x+\frac{20}{5}=-x+14+\frac{4}{5}x$$

Divide 20 by 5 to get 4.

$$\frac{1}{5}x+4=-x+14+\frac{4}{5}x$$

Add x to both sides.

$$\frac{1}{5}x+4+x=14+\frac{4}{5}x$$

Combine \frac{1}{5}x and x to get \frac{6}{5}x.

$$\frac{6}{5}x+4=14+\frac{4}{5}x$$

Subtract \frac{4}{5}x from both sides.

$$\frac{6}{5}x+4-\frac{4}{5}x=14$$

Combine \frac{6}{5}x and -\frac{4}{5}x to get \frac{2}{5}x.

$$\frac{2}{5}x+4=14$$

Subtract 4 from both sides.

$$\frac{2}{5}x=14-4$$

Subtract 4 from 14 to get 10.

$$\frac{2}{5}x=10$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$x=10\times \frac{5}{2}$$

Express 10\times \frac{5}{2} as a single fraction.

$$x=\frac{10\times 5}{2}$$

Multiply 10 and 5 to get 50.

$$x=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$x=25$$