Solve 1/2x-5/14x+1/2=5/7-frac{2}{7}x

$$\frac { 1 } { 2 } x - \frac { 5 } { 14 } x + \frac { 1 } { 2 } = \frac { 5 } { 7 } - \frac { 2 } { 7 } x$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Combine \frac{1}{2}x and -\frac{5}{14}x to get \frac{1}{7}x.

$$\frac{1}{7}x+\frac{1}{2}=\frac{5}{7}-\frac{2}{7}x$$

Add \frac{2}{7}x to both sides.

$$\frac{1}{7}x+\frac{1}{2}+\frac{2}{7}x=\frac{5}{7}$$

Combine \frac{1}{7}x and \frac{2}{7}x to get \frac{3}{7}x.

$$\frac{3}{7}x+\frac{1}{2}=\frac{5}{7}$$

Subtract \frac{1}{2} from both sides.

$$\frac{3}{7}x=\frac{5}{7}-\frac{1}{2}$$

Least common multiple of 7 and 2 is 14. Convert \frac{5}{7} and \frac{1}{2} to fractions with denominator 14.

$$\frac{3}{7}x=\frac{10}{14}-\frac{7}{14}$$

Since \frac{10}{14} and \frac{7}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{7}x=\frac{10-7}{14}$$

Subtract 7 from 10 to get 3.

$$\frac{3}{7}x=\frac{3}{14}$$

Multiply both sides by \frac{7}{3}, the reciprocal of \frac{3}{7}.

$$x=\frac{3}{14}\times \frac{7}{3}$$

Multiply \frac{3}{14} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\times 7}{14\times 3}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{7}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

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