Solve 1/20x+1/12(14-x)=1

$$\frac{ 1 }{ 20 } x+ \frac{ 1 }{ 12 } (14-x)=1$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{12} by 14-x.

$$\frac{1}{20}x+\frac{1}{12}\times 14+\frac{1}{12}\left(-1\right)x=1$$

Multiply \frac{1}{12} and 14 to get \frac{14}{12}.

$$\frac{1}{20}x+\frac{14}{12}+\frac{1}{12}\left(-1\right)x=1$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{20}x+\frac{7}{6}+\frac{1}{12}\left(-1\right)x=1$$

Multiply \frac{1}{12} and -1 to get -\frac{1}{12}.

$$\frac{1}{20}x+\frac{7}{6}-\frac{1}{12}x=1$$

Combine \frac{1}{20}x and -\frac{1}{12}x to get -\frac{1}{30}x.

$$-\frac{1}{30}x+\frac{7}{6}=1$$

Subtract \frac{7}{6} from both sides.

$$-\frac{1}{30}x=1-\frac{7}{6}$$

Convert 1 to fraction \frac{6}{6}.

$$-\frac{1}{30}x=\frac{6}{6}-\frac{7}{6}$$

Since \frac{6}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{30}x=\frac{6-7}{6}$$

Subtract 7 from 6 to get -1.

$$-\frac{1}{30}x=-\frac{1}{6}$$

Multiply both sides by -30, the reciprocal of -\frac{1}{30}.

$$x=-\frac{1}{6}\left(-30\right)$$

Express -\frac{1}{6}\left(-30\right) as a single fraction.

$$x=\frac{-\left(-30\right)}{6}$$

Multiply -1 and -30 to get 30.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$