Solve (24/6+54/3):[(5/2-1/6)*(frac{3}{2}+frac{1}{4})-frac{1}{12}]=(frac{3}{4}+x):x

$$( \frac { 24 } { 6 } + \frac { 54 } { 3 } ) : [ ( \frac { 5 } { 2 } - \frac { 1 } { 6 } ) \cdot ( \frac { 3 } { 2 } + \frac { 1 } { 4 } ) - \frac { 1 } { 12 } ] = ( \frac { 3 } { 4 } + x ) : x$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

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.

$$\frac{1}{4}x\left(\frac{24}{6}+\frac{54}{3}\right)=\frac{3}{4}+x$$

Divide 24 by 6 to get 4.

$$\frac{1}{4}x\left(4+\frac{54}{3}\right)=\frac{3}{4}+x$$

Divide 54 by 3 to get 18.

$$\frac{1}{4}x\left(4+18\right)=\frac{3}{4}+x$$

Add 4 and 18 to get 22.

$$\frac{1}{4}x\times 22=\frac{3}{4}+x$$

Multiply \frac{1}{4} and 22 to get \frac{22}{4}.

$$\frac{22}{4}x=\frac{3}{4}+x$$

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$\frac{11}{2}x=\frac{3}{4}+x$$

Subtract x from both sides.

$$\frac{11}{2}x-x=\frac{3}{4}$$

Combine \frac{11}{2}x and -x to get \frac{9}{2}x.

$$\frac{9}{2}x=\frac{3}{4}$$

Multiply both sides by \frac{2}{9}, the reciprocal of \frac{9}{2}.

$$x=\frac{3}{4}\times \frac{2}{9}$$

Multiply \frac{3}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\times 2}{4\times 9}$$

Do the multiplications in the fraction \frac{3\times 2}{4\times 9}.

$$x=\frac{6}{36}$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$x=\frac{1}{6}$$