Solve (x-1)(1/10+1/15)=1/12

$$(x-1)( \frac{ 1 }{ 10 } + \frac{ 1 }{ 15 } )= \frac{ 1 }{ 12 }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Least common multiple of 10 and 15 is 30. Convert \frac{1}{10} and \frac{1}{15} to fractions with denominator 30.

$$\left(x-1\right)\left(\frac{3}{30}+\frac{2}{30}\right)=\frac{1}{12}$$

Since \frac{3}{30} and \frac{2}{30} have the same denominator, add them by adding their numerators.

$$\left(x-1\right)\times \frac{3+2}{30}=\frac{1}{12}$$

Add 3 and 2 to get 5.

$$\left(x-1\right)\times \frac{5}{30}=\frac{1}{12}$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\left(x-1\right)\times \frac{1}{6}=\frac{1}{12}$$

Use the distributive property to multiply x-1 by \frac{1}{6}.

$$x\times \frac{1}{6}-\frac{1}{6}=\frac{1}{12}$$

Add \frac{1}{6} to both sides.

$$x\times \frac{1}{6}=\frac{1}{12}+\frac{1}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{1}{12} and \frac{1}{6} to fractions with denominator 12.

$$x\times \frac{1}{6}=\frac{1}{12}+\frac{2}{12}$$

Since \frac{1}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$x\times \frac{1}{6}=\frac{1+2}{12}$$

Add 1 and 2 to get 3.

$$x\times \frac{1}{6}=\frac{3}{12}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$x\times \frac{1}{6}=\frac{1}{4}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=\frac{1}{4}\times 6$$

Multiply \frac{1}{4} and 6 to get \frac{6}{4}.

$$x=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{3}{2}$$