Solve (17/3-4.3):x=(5/4*8/10-4/9:2):(frac{5}{4}+frac{2}{5}-frac{1}{4})

$$( \frac { 17 } { 3 } - 4.3 ) : x = ( \frac { 5 } { 4 } \cdot \frac { 8 } { 10 } - \frac { 4 } { 9 } : 2 ) : ( \frac { 5 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 4 } )$$

Solve for x

$$x=2.46$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{17}{3}-4.3=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Convert decimal number 4.3 to fraction \frac{43}{10}.

$$\frac{17}{3}-\frac{43}{10}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Least common multiple of 3 and 10 is 30. Convert \frac{17}{3} and \frac{43}{10} to fractions with denominator 30.

$$\frac{170}{30}-\frac{129}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Since \frac{170}{30} and \frac{129}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{170-129}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Subtract 129 from 170 to get 41.

$$\frac{41}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{41}{30}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{4}{5}-\frac{\frac{4}{9}}{2}\right)$$

Cancel out \frac{5}{4} and its reciprocal \frac{4}{5}.

$$\frac{41}{30}=\frac{5}{7}x\left(1-\frac{\frac{4}{9}}{2}\right)$$

Express \frac{\frac{4}{9}}{2} as a single fraction.

$$\frac{41}{30}=\frac{5}{7}x\left(1-\frac{4}{9\times 2}\right)$$

Multiply 9 and 2 to get 18.

$$\frac{41}{30}=\frac{5}{7}x\left(1-\frac{4}{18}\right)$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$\frac{41}{30}=\frac{5}{7}x\left(1-\frac{2}{9}\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{41}{30}=\frac{5}{7}x\left(\frac{9}{9}-\frac{2}{9}\right)$$

Since \frac{9}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{30}=\frac{5}{7}x\times \frac{9-2}{9}$$

Subtract 2 from 9 to get 7.

$$\frac{41}{30}=\frac{5}{7}x\times \frac{7}{9}$$

Multiply \frac{5}{7} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41}{30}=\frac{5\times 7}{7\times 9}x$$

Cancel out 7 in both numerator and denominator.

$$\frac{41}{30}=\frac{5}{9}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{5}{9}x=\frac{41}{30}$$

Multiply both sides by \frac{9}{5}, the reciprocal of \frac{5}{9}.

$$x=\frac{41}{30}\times \frac{9}{5}$$

Multiply \frac{41}{30} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{41\times 9}{30\times 5}$$

Do the multiplications in the fraction \frac{41\times 9}{30\times 5}.

$$x=\frac{369}{150}$$

Reduce the fraction \frac{369}{150} to lowest terms by extracting and canceling out 3.

$$x=\frac{123}{50}$$