Solve 3/2-x=2/8-4/5

$$\frac { 3 } { 2 } - x = \frac { 2 } { 8 } - \frac { 4 } { 5 }$$

Solve for x

$$x = \frac{41}{20} = 2\frac{1}{20} = 2.05$$

Steps for Solving Linear Equation

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

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

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{3}{2}-x=\frac{5}{20}-\frac{16}{20}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-x=\frac{5-16}{20}$$

Subtract 16 from 5 to get -11.

$$\frac{3}{2}-x=-\frac{11}{20}$$

Subtract \frac{3}{2} from both sides.

$$-x=-\frac{11}{20}-\frac{3}{2}$$

Least common multiple of 20 and 2 is 20. Convert -\frac{11}{20} and \frac{3}{2} to fractions with denominator 20.

$$-x=-\frac{11}{20}-\frac{30}{20}$$

Since -\frac{11}{20} and \frac{30}{20} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{-11-30}{20}$$

Subtract 30 from -11 to get -41.

$$-x=-\frac{41}{20}$$

Multiply both sides by -1.

$$x=\frac{41}{20}$$