Solve 1/2=1/5+P-1/5*P

$$\frac { 1 } { 2 } = \frac { 1 } { 5 } + P - \frac { 1 } { 5 } \times P$$

Solve for P

$$P=\frac{3}{8}=0.375$$

Steps for Solving Linear Equation

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

$$\frac{1}{2}=\frac{1}{5}+\frac{4}{5}P$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{5}+\frac{4}{5}P=\frac{1}{2}$$

Subtract \frac{1}{5} from both sides.

$$\frac{4}{5}P=\frac{1}{2}-\frac{1}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{4}{5}P=\frac{5}{10}-\frac{2}{10}$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}P=\frac{5-2}{10}$$

Subtract 2 from 5 to get 3.

$$\frac{4}{5}P=\frac{3}{10}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.

$$P=\frac{3}{10}\times \frac{5}{4}$$

Multiply \frac{3}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$P=\frac{3\times 5}{10\times 4}$$

Do the multiplications in the fraction \frac{3\times 5}{10\times 4}.

$$P=\frac{15}{40}$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$P=\frac{3}{8}$$