Solve x:(1/2+3/2)=(3/2-1/4):(frac{1}{4}+frac{6}{8})

$$x : ( \frac { 1 } { 2 } + \frac { 3 } { 2 } ) = ( \frac { 3 } { 2 } - \frac { 1 } { 4 } ) : ( \frac { 1 } { 4 } + \frac { 6 } { 8 } )$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Since \frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{1+3}{2}}=\frac{\frac{3}{2}-\frac{1}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Add 1 and 3 to get 4.

$$\frac{x}{\frac{4}{2}}=\frac{\frac{3}{2}-\frac{1}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Divide 4 by 2 to get 2.

$$\frac{x}{2}=\frac{\frac{3}{2}-\frac{1}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{x}{2}=\frac{\frac{6}{4}-\frac{1}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{2}=\frac{\frac{6-1}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Subtract 1 from 6 to get 5.

$$\frac{x}{2}=\frac{\frac{5}{4}}{\frac{1}{4}+\frac{6}{8}}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{x}{2}=\frac{\frac{5}{4}}{\frac{1}{4}+\frac{3}{4}}$$

Since \frac{1}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{x}{2}=\frac{\frac{5}{4}}{\frac{1+3}{4}}$$

Add 1 and 3 to get 4.

$$\frac{x}{2}=\frac{\frac{5}{4}}{\frac{4}{4}}$$

Divide 4 by 4 to get 1.

$$\frac{x}{2}=\frac{\frac{5}{4}}{1}$$

Anything divided by one gives itself.

$$\frac{x}{2}=\frac{5}{4}$$

Multiply both sides by 2.

$$x=\frac{5}{4}\times 2$$

Express \frac{5}{4}\times 2 as a single fraction.

$$x=\frac{5\times 2}{4}$$

Multiply 5 and 2 to get 10.

$$x=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{2}$$