Solve 12/28x+12/44left(10-xright)=3.6

$$\frac{ 12 }{ 28 } x+ \frac{ 12 }{ 44 } \left( 10-x \right) = 3.6$$

Solve for x

$$x=5.6$$

Steps for Solving Linear Equation

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

$$\frac{3}{7}x+\frac{12}{44}\left(10-x\right)=3.6$$

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

$$\frac{3}{7}x+\frac{3}{11}\left(10-x\right)=3.6$$

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

$$\frac{3}{7}x+\frac{3}{11}\times 10+\frac{3}{11}\left(-1\right)x=3.6$$

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

$$\frac{3}{7}x+\frac{3\times 10}{11}+\frac{3}{11}\left(-1\right)x=3.6$$

Multiply 3 and 10 to get 30.

$$\frac{3}{7}x+\frac{30}{11}+\frac{3}{11}\left(-1\right)x=3.6$$

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

$$\frac{3}{7}x+\frac{30}{11}-\frac{3}{11}x=3.6$$

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

$$\frac{12}{77}x+\frac{30}{11}=3.6$$

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

$$\frac{12}{77}x=3.6-\frac{30}{11}$$

Convert decimal number 3.6 to fraction \frac{36}{10}. Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{12}{77}x=\frac{18}{5}-\frac{30}{11}$$

Least common multiple of 5 and 11 is 55. Convert \frac{18}{5} and \frac{30}{11} to fractions with denominator 55.

$$\frac{12}{77}x=\frac{198}{55}-\frac{150}{55}$$

Since \frac{198}{55} and \frac{150}{55} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{77}x=\frac{198-150}{55}$$

Subtract 150 from 198 to get 48.

$$\frac{12}{77}x=\frac{48}{55}$$

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

$$x=\frac{48}{55}\times \frac{77}{12}$$

Multiply \frac{48}{55} times \frac{77}{12} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{48\times 77}{55\times 12}$$

Do the multiplications in the fraction \frac{48\times 77}{55\times 12}.

$$x=\frac{3696}{660}$$

Reduce the fraction \frac{3696}{660} to lowest terms by extracting and canceling out 132.

$$x=\frac{28}{5}$$