Solve (24/5-1):x=(11/4+3/8+5/6):(frac{5}{12}+frac{5}{4})

$$( \frac { 24 } { 5 } - 1 ) : x = ( \frac { 11 } { 4 } + \frac { 3 } { 8 } + \frac { 5 } { 6 } ) : ( \frac { 5 } { 12 } + \frac { 5 } { 4 } )$$

Solve for x

$$x = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

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.

$$\frac{24}{5}-1=\frac{3}{5}x\left(\frac{11}{4}+\frac{3}{8}+\frac{5}{6}\right)$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{24}{5}-\frac{5}{5}=\frac{3}{5}x\left(\frac{11}{4}+\frac{3}{8}+\frac{5}{6}\right)$$

Since \frac{24}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-5}{5}=\frac{3}{5}x\left(\frac{11}{4}+\frac{3}{8}+\frac{5}{6}\right)$$

Subtract 5 from 24 to get 19.

$$\frac{19}{5}=\frac{3}{5}x\left(\frac{11}{4}+\frac{3}{8}+\frac{5}{6}\right)$$

Least common multiple of 4 and 8 is 8. Convert \frac{11}{4} and \frac{3}{8} to fractions with denominator 8.

$$\frac{19}{5}=\frac{3}{5}x\left(\frac{22}{8}+\frac{3}{8}+\frac{5}{6}\right)$$

Since \frac{22}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{19}{5}=\frac{3}{5}x\left(\frac{22+3}{8}+\frac{5}{6}\right)$$

Add 22 and 3 to get 25.

$$\frac{19}{5}=\frac{3}{5}x\left(\frac{25}{8}+\frac{5}{6}\right)$$

Least common multiple of 8 and 6 is 24. Convert \frac{25}{8} and \frac{5}{6} to fractions with denominator 24.

$$\frac{19}{5}=\frac{3}{5}x\left(\frac{75}{24}+\frac{20}{24}\right)$$

Since \frac{75}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{19}{5}=\frac{3}{5}x\times \frac{75+20}{24}$$

Add 75 and 20 to get 95.

$$\frac{19}{5}=\frac{3}{5}x\times \frac{95}{24}$$

Multiply \frac{3}{5} times \frac{95}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19}{5}=\frac{3\times 95}{5\times 24}x$$

Do the multiplications in the fraction \frac{3\times 95}{5\times 24}.

$$\frac{19}{5}=\frac{285}{120}x$$

Reduce the fraction \frac{285}{120} to lowest terms by extracting and canceling out 15.

$$\frac{19}{5}=\frac{19}{8}x$$

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

$$\frac{19}{8}x=\frac{19}{5}$$

Multiply both sides by \frac{8}{19}, the reciprocal of \frac{19}{8}.

$$x=\frac{19}{5}\times \frac{8}{19}$$

Multiply \frac{19}{5} times \frac{8}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{19\times 8}{5\times 19}$$

Cancel out 19 in both numerator and denominator.

$$x=\frac{8}{5}$$