Solve (1/15+1/12)*3+1/12x=1

$$( \frac { 1 } { 15 } + \frac { 1 } { 12 } ) \times 3 + \frac { 1 } { 12 } x = 1$$

Solve for x

$$x = \frac{33}{5} = 6\frac{3}{5} = 6.6$$

Steps for Solving Linear Equation

Least common multiple of 15 and 12 is 60. Convert \frac{1}{15} and \frac{1}{12} to fractions with denominator 60.

$$\left(\frac{4}{60}+\frac{5}{60}\right)\times 3+\frac{1}{12}x=1$$

Since \frac{4}{60} and \frac{5}{60} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{60}\times 3+\frac{1}{12}x=1$$

Add 4 and 5 to get 9.

$$\frac{9}{60}\times 3+\frac{1}{12}x=1$$

Reduce the fraction \frac{9}{60} to lowest terms by extracting and canceling out 3.

$$\frac{3}{20}\times 3+\frac{1}{12}x=1$$

Express \frac{3}{20}\times 3 as a single fraction.

$$\frac{3\times 3}{20}+\frac{1}{12}x=1$$

Multiply 3 and 3 to get 9.

$$\frac{9}{20}+\frac{1}{12}x=1$$

Subtract \frac{9}{20} from both sides.

$$\frac{1}{12}x=1-\frac{9}{20}$$

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

$$\frac{1}{12}x=\frac{20}{20}-\frac{9}{20}$$

Since \frac{20}{20} and \frac{9}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}x=\frac{20-9}{20}$$

Subtract 9 from 20 to get 11.

$$\frac{1}{12}x=\frac{11}{20}$$

Multiply both sides by 12, the reciprocal of \frac{1}{12}.

$$x=\frac{11}{20}\times 12$$

Express \frac{11}{20}\times 12 as a single fraction.

$$x=\frac{11\times 12}{20}$$

Multiply 11 and 12 to get 132.

$$x=\frac{132}{20}$$

Reduce the fraction \frac{132}{20} to lowest terms by extracting and canceling out 4.

$$x=\frac{33}{5}$$