Solve 1/2x+3/10+2x=1/5x+13/5

$$\frac { 1 } { 2 } x + \frac { 3 } { 10 } + 2 x = \frac { 1 } { 5 } x + \frac { 13 } { 5 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

$$\frac{5}{2}x+\frac{3}{10}=\frac{1}{5}x+\frac{13}{5}$$

Subtract \frac{1}{5}x from both sides.

$$\frac{5}{2}x+\frac{3}{10}-\frac{1}{5}x=\frac{13}{5}$$

Combine \frac{5}{2}x and -\frac{1}{5}x to get \frac{23}{10}x.

$$\frac{23}{10}x+\frac{3}{10}=\frac{13}{5}$$

Subtract \frac{3}{10} from both sides.

$$\frac{23}{10}x=\frac{13}{5}-\frac{3}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{13}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{23}{10}x=\frac{26}{10}-\frac{3}{10}$$

Since \frac{26}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23}{10}x=\frac{26-3}{10}$$

Subtract 3 from 26 to get 23.

$$\frac{23}{10}x=\frac{23}{10}$$

Multiply both sides by \frac{10}{23}, the reciprocal of \frac{23}{10}.

$$x=\frac{23}{10}\times \frac{10}{23}$$

Cancel out \frac{23}{10} and its reciprocal \frac{10}{23}.

$$x=1$$