Solve (3/4-5/2):x=(4/3+5/2):(frac{7}{2}+frac{5}{4})

$$( \frac { 3 } { 4 } - \frac { 5 } { 2 } ) : x = ( \frac { 4 } { 3 } + \frac { 5 } { 2 } ) : ( \frac { 7 } { 2 } + \frac { 5 } { 4 } )$$

Solve for x

$$x = -\frac{399}{184} = -2\frac{31}{184} \approx -2.168478261$$

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.

$$\frac{3}{4}-\frac{5}{2}=\frac{4}{19}x\left(\frac{4}{3}+\frac{5}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{3}{4}-\frac{10}{4}=\frac{4}{19}x\left(\frac{4}{3}+\frac{5}{2}\right)$$

Since \frac{3}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{4}=\frac{4}{19}x\left(\frac{4}{3}+\frac{5}{2}\right)$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{4}=\frac{4}{19}x\left(\frac{4}{3}+\frac{5}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{7}{4}=\frac{4}{19}x\left(\frac{8}{6}+\frac{15}{6}\right)$$

Since \frac{8}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$-\frac{7}{4}=\frac{4}{19}x\times \frac{8+15}{6}$$

Add 8 and 15 to get 23.

$$-\frac{7}{4}=\frac{4}{19}x\times \frac{23}{6}$$

Multiply \frac{4}{19} times \frac{23}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{7}{4}=\frac{4\times 23}{19\times 6}x$$

Do the multiplications in the fraction \frac{4\times 23}{19\times 6}.

$$-\frac{7}{4}=\frac{92}{114}x$$

Reduce the fraction \frac{92}{114} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{4}=\frac{46}{57}x$$

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

$$\frac{46}{57}x=-\frac{7}{4}$$

Multiply both sides by \frac{57}{46}, the reciprocal of \frac{46}{57}.

$$x=-\frac{7}{4}\times \frac{57}{46}$$

Multiply -\frac{7}{4} times \frac{57}{46} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\times 57}{4\times 46}$$

Do the multiplications in the fraction \frac{-7\times 57}{4\times 46}.

$$x=\frac{-399}{184}$$

Fraction \frac{-399}{184} can be rewritten as -\frac{399}{184} by extracting the negative sign.

$$x=-\frac{399}{184}$$