Solve x+(3.3-22/53x)*84/44=7.4

$$x + ( 3.3 - \frac { 22 } { 53 } x ) \cdot \frac { 84 } { 44 } = 7.4$$

Solve for x

$$x=5.3$$

Steps for Solving Linear Equation

Reduce the fraction \frac{84}{44} to lowest terms by extracting and canceling out 4.

$$x+\left(3.3-\frac{22}{53}x\right)\times \frac{21}{11}=7.4$$

Use the distributive property to multiply 3.3-\frac{22}{53}x by \frac{21}{11}.

$$x+3.3\times \frac{21}{11}-\frac{22}{53}x\times \frac{21}{11}=7.4$$

Convert decimal number 3.3 to fraction \frac{33}{10}.

$$x+\frac{33}{10}\times \frac{21}{11}-\frac{22}{53}x\times \frac{21}{11}=7.4$$

Multiply \frac{33}{10} times \frac{21}{11} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{33\times 21}{10\times 11}-\frac{22}{53}x\times \frac{21}{11}=7.4$$

Do the multiplications in the fraction \frac{33\times 21}{10\times 11}.

$$x+\frac{693}{110}-\frac{22}{53}x\times \frac{21}{11}=7.4$$

Reduce the fraction \frac{693}{110} to lowest terms by extracting and canceling out 11.

$$x+\frac{63}{10}-\frac{22}{53}x\times \frac{21}{11}=7.4$$

Multiply -\frac{22}{53} times \frac{21}{11} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{63}{10}+\frac{-22\times 21}{53\times 11}x=7.4$$

Do the multiplications in the fraction \frac{-22\times 21}{53\times 11}.

$$x+\frac{63}{10}+\frac{-462}{583}x=7.4$$

Reduce the fraction \frac{-462}{583} to lowest terms by extracting and canceling out 11.

$$x+\frac{63}{10}-\frac{42}{53}x=7.4$$

Combine x and -\frac{42}{53}x to get \frac{11}{53}x.

$$\frac{11}{53}x+\frac{63}{10}=7.4$$

Subtract \frac{63}{10} from both sides.

$$\frac{11}{53}x=7.4-\frac{63}{10}$$

Convert decimal number 7.4 to fraction \frac{74}{10}. Reduce the fraction \frac{74}{10} to lowest terms by extracting and canceling out 2.

$$\frac{11}{53}x=\frac{37}{5}-\frac{63}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{37}{5} and \frac{63}{10} to fractions with denominator 10.

$$\frac{11}{53}x=\frac{74}{10}-\frac{63}{10}$$

Since \frac{74}{10} and \frac{63}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{53}x=\frac{74-63}{10}$$

Subtract 63 from 74 to get 11.

$$\frac{11}{53}x=\frac{11}{10}$$

Multiply both sides by \frac{53}{11}, the reciprocal of \frac{11}{53}.

$$x=\frac{11}{10}\times \frac{53}{11}$$

Multiply \frac{11}{10} times \frac{53}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\times 53}{10\times 11}$$

Cancel out 11 in both numerator and denominator.

$$x=\frac{53}{10}$$