Solve 12/28x+12/44left(10-xright)=36

$$\frac{ 12 }{ 28 } x+ \frac{ 12 }{ 44 } \left( 10-x \right) = 36$$

Solve for x

$$x = \frac{427}{2} = 213\frac{1}{2} = 213.5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{12}{28} to lowest terms by extracting and canceling out 4.

$$\frac{3}{7}x+\frac{12}{44}\left(10-x\right)=36$$

Reduce the fraction \frac{12}{44} to lowest terms by extracting and canceling out 4.

$$\frac{3}{7}x+\frac{3}{11}\left(10-x\right)=36$$

Use the distributive property to multiply \frac{3}{11} by 10-x.

$$\frac{3}{7}x+\frac{3}{11}\times 10+\frac{3}{11}\left(-1\right)x=36$$

Express \frac{3}{11}\times 10 as a single fraction.

$$\frac{3}{7}x+\frac{3\times 10}{11}+\frac{3}{11}\left(-1\right)x=36$$

Multiply 3 and 10 to get 30.

$$\frac{3}{7}x+\frac{30}{11}+\frac{3}{11}\left(-1\right)x=36$$

Multiply \frac{3}{11} and -1 to get -\frac{3}{11}.

$$\frac{3}{7}x+\frac{30}{11}-\frac{3}{11}x=36$$

Combine \frac{3}{7}x and -\frac{3}{11}x to get \frac{12}{77}x.

$$\frac{12}{77}x+\frac{30}{11}=36$$

Subtract \frac{30}{11} from both sides.

$$\frac{12}{77}x=36-\frac{30}{11}$$

Convert 36 to fraction \frac{396}{11}.

$$\frac{12}{77}x=\frac{396}{11}-\frac{30}{11}$$

Since \frac{396}{11} and \frac{30}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{77}x=\frac{396-30}{11}$$

Subtract 30 from 396 to get 366.

$$\frac{12}{77}x=\frac{366}{11}$$

Multiply both sides by \frac{77}{12}, the reciprocal of \frac{12}{77}.

$$x=\frac{366}{11}\times \frac{77}{12}$$

Multiply \frac{366}{11} times \frac{77}{12} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{366\times 77}{11\times 12}$$

Do the multiplications in the fraction \frac{366\times 77}{11\times 12}.

$$x=\frac{28182}{132}$$

Reduce the fraction \frac{28182}{132} to lowest terms by extracting and canceling out 66.

$$x=\frac{427}{2}$$