Solve 2/21=1-17/20*(1-x)

$$\frac { 2 } { 21 } = 1 - \frac { 17 } { 20 } \times ( 1 - x )$$

Solve for x

$$x=-\frac{23}{357}\approx -0.06442577$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{17}{20} by 1-x.

$$\frac{2}{21}=1-\frac{17}{20}-\frac{17}{20}\left(-1\right)x$$

Multiply -\frac{17}{20} and -1 to get \frac{17}{20}.

$$\frac{2}{21}=1-\frac{17}{20}+\frac{17}{20}x$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{2}{21}=\frac{20}{20}-\frac{17}{20}+\frac{17}{20}x$$

Since \frac{20}{20} and \frac{17}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{21}=\frac{20-17}{20}+\frac{17}{20}x$$

Subtract 17 from 20 to get 3.

$$\frac{2}{21}=\frac{3}{20}+\frac{17}{20}x$$

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

$$\frac{3}{20}+\frac{17}{20}x=\frac{2}{21}$$

Subtract \frac{3}{20} from both sides.

$$\frac{17}{20}x=\frac{2}{21}-\frac{3}{20}$$

Least common multiple of 21 and 20 is 420. Convert \frac{2}{21} and \frac{3}{20} to fractions with denominator 420.

$$\frac{17}{20}x=\frac{40}{420}-\frac{63}{420}$$

Since \frac{40}{420} and \frac{63}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{20}x=\frac{40-63}{420}$$

Subtract 63 from 40 to get -23.

$$\frac{17}{20}x=-\frac{23}{420}$$

Multiply both sides by \frac{20}{17}, the reciprocal of \frac{17}{20}.

$$x=-\frac{23}{420}\times \frac{20}{17}$$

Multiply -\frac{23}{420} times \frac{20}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-23\times 20}{420\times 17}$$

Do the multiplications in the fraction \frac{-23\times 20}{420\times 17}.

$$x=\frac{-460}{7140}$$

Reduce the fraction \frac{-460}{7140} to lowest terms by extracting and canceling out 20.

$$x=-\frac{23}{357}$$