Solve 3/5-2/4+4/5X-2/3=frac{1}{2}

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

Solve for X

$$X = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{6}{10}-\frac{5}{10}+\frac{4}{5}X-\frac{2}{3}=\frac{1}{2}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{10}+\frac{4}{5}X-\frac{2}{3}=\frac{1}{2}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{10}+\frac{4}{5}X-\frac{2}{3}=\frac{1}{2}$$

Least common multiple of 10 and 3 is 30. Convert \frac{1}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{3}{30}+\frac{4}{5}X-\frac{20}{30}=\frac{1}{2}$$

Since \frac{3}{30} and \frac{20}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-20}{30}+\frac{4}{5}X=\frac{1}{2}$$

Subtract 20 from 3 to get -17.

$$-\frac{17}{30}+\frac{4}{5}X=\frac{1}{2}$$

Add \frac{17}{30} to both sides.

$$\frac{4}{5}X=\frac{1}{2}+\frac{17}{30}$$

Least common multiple of 2 and 30 is 30. Convert \frac{1}{2} and \frac{17}{30} to fractions with denominator 30.

$$\frac{4}{5}X=\frac{15}{30}+\frac{17}{30}$$

Since \frac{15}{30} and \frac{17}{30} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}X=\frac{15+17}{30}$$

Add 15 and 17 to get 32.

$$\frac{4}{5}X=\frac{32}{30}$$

Reduce the fraction \frac{32}{30} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}X=\frac{16}{15}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.

$$X=\frac{16}{15}\times \frac{5}{4}$$

Multiply \frac{16}{15} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$X=\frac{16\times 5}{15\times 4}$$

Do the multiplications in the fraction \frac{16\times 5}{15\times 4}.

$$X=\frac{80}{60}$$

Reduce the fraction \frac{80}{60} to lowest terms by extracting and canceling out 20.

$$X=\frac{4}{3}$$