Solve 1/2x+2/5=1/3x+3/4

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

Solve for x

$$x = \frac{21}{10} = 2\frac{1}{10} = 2.1$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}x from both sides.

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

Combine \frac{1}{2}x and -\frac{1}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x+\frac{2}{5}=\frac{3}{4}$$

Subtract \frac{2}{5} from both sides.

$$\frac{1}{6}x=\frac{3}{4}-\frac{2}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{1}{6}x=\frac{15}{20}-\frac{8}{20}$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}x=\frac{15-8}{20}$$

Subtract 8 from 15 to get 7.

$$\frac{1}{6}x=\frac{7}{20}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$x=\frac{7}{20}\times 6$$

Express \frac{7}{20}\times 6 as a single fraction.

$$x=\frac{7\times 6}{20}$$

Multiply 7 and 6 to get 42.

$$x=\frac{42}{20}$$

Reduce the fraction \frac{42}{20} to lowest terms by extracting and canceling out 2.

$$x=\frac{21}{10}$$