Solve 7(17/3-43):x=(5/4*8/10-4/9:2):(frac{5}{4}+frac{2}{5}-frac{1}{4})

$$7 ( \frac { 17 } { 3 } - 43 ) : x = ( \frac { 5 } { 4 } \cdot \frac { 8 } { 10 } - \frac { 4 } { 9 } : 2 ) : ( \frac { 5 } { 4 } + \frac { 2 } { 5 } - \frac { 1 } { 4 } )$$

Solve for x

$$x = -\frac{2352}{5} = -470\frac{2}{5} = -470.4$$

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.

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

Convert 43 to fraction \frac{129}{3}.

$$7\left(\frac{17}{3}-\frac{129}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Since \frac{17}{3} and \frac{129}{3} have the same denominator, subtract them by subtracting their numerators.

$$7\times \frac{17-129}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Subtract 129 from 17 to get -112.

$$7\left(-\frac{112}{3}\right)=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Express 7\left(-\frac{112}{3}\right) as a single fraction.

$$\frac{7\left(-112\right)}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Multiply 7 and -112 to get -784.

$$\frac{-784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

Fraction \frac{-784}{3} can be rewritten as -\frac{784}{3} by extracting the negative sign.

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{8}{10}-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{5}{4}\times \frac{4}{5}-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{\frac{4}{9}}{2}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{9\times 2}\right)$$

Multiply 9 and 2 to get 18.

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{4}{18}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(1-\frac{2}{9}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\left(\frac{9}{9}-\frac{2}{9}\right)$$

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

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{9-2}{9}$$

Subtract 2 from 9 to get 7.

$$-\frac{784}{3}=\frac{5}{7}x\times \frac{7}{9}$$

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

$$-\frac{784}{3}=\frac{5\times 7}{7\times 9}x$$

Cancel out 7 in both numerator and denominator.

$$-\frac{784}{3}=\frac{5}{9}x$$

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

$$\frac{5}{9}x=-\frac{784}{3}$$

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

$$x=-\frac{784}{3}\times \frac{9}{5}$$

Multiply -\frac{784}{3} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-784\times 9}{3\times 5}$$

Do the multiplications in the fraction \frac{-784\times 9}{3\times 5}.

$$x=\frac{-7056}{15}$$

Reduce the fraction \frac{-7056}{15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{2352}{5}$$