Solve 71/15+left(x-7right)left(1/15+1/12right)=1

$$7 \frac{ 1 }{ 15 } + \left( x-7 \right) \left( \frac{ 1 }{ 15 } + \frac{ 1 }{ 12 } \right) = 1$$

Solve for x

$$x = -\frac{301}{9} = -33\frac{4}{9} \approx -33.444444444$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 15,12.

$$4\left(7\times 15+1\right)+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Multiply 7 and 15 to get 105.

$$4\left(105+1\right)+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Add 105 and 1 to get 106.

$$4\times 106+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

Multiply 4 and 106 to get 424.

$$424+60\left(x-7\right)\left(\frac{1}{15}+\frac{1}{12}\right)=60$$

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

$$424+60\left(x-7\right)\left(\frac{4}{60}+\frac{5}{60}\right)=60$$

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

$$424+60\left(x-7\right)\times \frac{4+5}{60}=60$$

Add 4 and 5 to get 9.

$$424+60\left(x-7\right)\times \frac{9}{60}=60$$

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

$$424+60\left(x-7\right)\times \frac{3}{20}=60$$

Express 60\times \frac{3}{20} as a single fraction.

$$424+\frac{60\times 3}{20}\left(x-7\right)=60$$

Multiply 60 and 3 to get 180.

$$424+\frac{180}{20}\left(x-7\right)=60$$

Divide 180 by 20 to get 9.

$$424+9\left(x-7\right)=60$$

Use the distributive property to multiply 9 by x-7.

$$424+9x-63=60$$

Subtract 63 from 424 to get 361.

$$361+9x=60$$

Subtract 361 from both sides.

$$9x=60-361$$

Subtract 361 from 60 to get -301.

$$9x=-301$$

Divide both sides by 9.

$$x=\frac{-301}{9}$$

Fraction \frac{-301}{9} can be rewritten as -\frac{301}{9} by extracting the negative sign.

$$x=-\frac{301}{9}$$