Solve 1x_{1}=frac{1/2/frac{1{2}+(1-1/2)}}{2/10}

$$1 x _ { 1 } = \frac { \frac { \frac { 1 } { 2 } } { \frac { 1 } { 2 } + ( 1 - \frac { 1 } { 2 } ) } } { \frac { 2 } { 10 } }$$

Solve for x_1

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

Steps for Solving Linear Equation

Divide \frac{\frac{1}{2}}{\frac{1}{2}+1-\frac{1}{2}} by \frac{2}{10} by multiplying \frac{\frac{1}{2}}{\frac{1}{2}+1-\frac{1}{2}} by the reciprocal of \frac{2}{10}.

$$1x_{1}=\frac{\frac{1}{2}\times 10}{\left(\frac{1}{2}+1-\frac{1}{2}\right)\times 2}$$

Cancel out 2 in both numerator and denominator.

$$1x_{1}=\frac{\frac{1}{2}\times 5}{\frac{1}{2}+1-\frac{1}{2}}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$1x_{1}=\frac{\frac{5}{2}}{\frac{1}{2}+1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$1x_{1}=\frac{\frac{5}{2}}{\frac{1}{2}+\frac{2}{2}-\frac{1}{2}}$$

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

$$1x_{1}=\frac{\frac{5}{2}}{\frac{1+2}{2}-\frac{1}{2}}$$

Add 1 and 2 to get 3.

$$1x_{1}=\frac{\frac{5}{2}}{\frac{3}{2}-\frac{1}{2}}$$

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

$$1x_{1}=\frac{\frac{5}{2}}{\frac{3-1}{2}}$$

Subtract 1 from 3 to get 2.

$$1x_{1}=\frac{\frac{5}{2}}{\frac{2}{2}}$$

Divide 2 by 2 to get 1.

$$1x_{1}=\frac{\frac{5}{2}}{1}$$

Anything divided by one gives itself.

$$1x_{1}=\frac{5}{2}$$

Reorder the terms.

$$x_{1}=\frac{5}{2}$$