Solve 1/25(20-x)=4/25x-3/5

$$\frac { 1 } { 25 } ( 20 - x ) = \frac { 4 } { 25 } x - \frac { 3 } { 5 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{25} by 20-x.

$$\frac{1}{25}\times 20+\frac{1}{25}\left(-1\right)x=\frac{4}{25}x-\frac{3}{5}$$

Multiply \frac{1}{25} and 20 to get \frac{20}{25}.

$$\frac{20}{25}+\frac{1}{25}\left(-1\right)x=\frac{4}{25}x-\frac{3}{5}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}+\frac{1}{25}\left(-1\right)x=\frac{4}{25}x-\frac{3}{5}$$

Multiply \frac{1}{25} and -1 to get -\frac{1}{25}.

$$\frac{4}{5}-\frac{1}{25}x=\frac{4}{25}x-\frac{3}{5}$$

Subtract \frac{4}{25}x from both sides.

$$\frac{4}{5}-\frac{1}{25}x-\frac{4}{25}x=-\frac{3}{5}$$

Combine -\frac{1}{25}x and -\frac{4}{25}x to get -\frac{1}{5}x.

$$\frac{4}{5}-\frac{1}{5}x=-\frac{3}{5}$$

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

$$-\frac{1}{5}x=-\frac{3}{5}-\frac{4}{5}$$

Since -\frac{3}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{5}x=\frac{-3-4}{5}$$

Subtract 4 from -3 to get -7.

$$-\frac{1}{5}x=-\frac{7}{5}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$x=-\frac{7}{5}\left(-5\right)$$

Express -\frac{7}{5}\left(-5\right) as a single fraction.

$$x=\frac{-7\left(-5\right)}{5}$$

Multiply -7 and -5 to get 35.

$$x=\frac{35}{5}$$

Divide 35 by 5 to get 7.

$$x=7$$