Solve 20*22%+x=40%(20+x)

$$20 \times 22 \% +x=40 \% (20+x)$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Reduce the fraction \frac{22}{100} to lowest terms by extracting and canceling out 2.

$$20\times \frac{11}{50}+x=\frac{40}{100}\left(20+x\right)$$

Express 20\times \frac{11}{50} as a single fraction.

$$\frac{20\times 11}{50}+x=\frac{40}{100}\left(20+x\right)$$

Multiply 20 and 11 to get 220.

$$\frac{220}{50}+x=\frac{40}{100}\left(20+x\right)$$

Reduce the fraction \frac{220}{50} to lowest terms by extracting and canceling out 10.

$$\frac{22}{5}+x=\frac{40}{100}\left(20+x\right)$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{22}{5}+x=\frac{2}{5}\left(20+x\right)$$

Use the distributive property to multiply \frac{2}{5} by 20+x.

$$\frac{22}{5}+x=\frac{2}{5}\times 20+\frac{2}{5}x$$

Express \frac{2}{5}\times 20 as a single fraction.

$$\frac{22}{5}+x=\frac{2\times 20}{5}+\frac{2}{5}x$$

Multiply 2 and 20 to get 40.

$$\frac{22}{5}+x=\frac{40}{5}+\frac{2}{5}x$$

Divide 40 by 5 to get 8.

$$\frac{22}{5}+x=8+\frac{2}{5}x$$

Subtract \frac{2}{5}x from both sides.

$$\frac{22}{5}+x-\frac{2}{5}x=8$$

Combine x and -\frac{2}{5}x to get \frac{3}{5}x.

$$\frac{22}{5}+\frac{3}{5}x=8$$

Subtract \frac{22}{5} from both sides.

$$\frac{3}{5}x=8-\frac{22}{5}$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{3}{5}x=\frac{40}{5}-\frac{22}{5}$$

Since \frac{40}{5} and \frac{22}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}x=\frac{40-22}{5}$$

Subtract 22 from 40 to get 18.

$$\frac{3}{5}x=\frac{18}{5}$$

Multiply both sides by \frac{5}{3}, the reciprocal of \frac{3}{5}.

$$x=\frac{18}{5}\times \frac{5}{3}$$

Multiply \frac{18}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{18\times 5}{5\times 3}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$x=6$$