Solve 1/3x+1/4=2/5*(x-3/4)

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

Solve for x

$$x = \frac{33}{4} = 8\frac{1}{4} = 8.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by x-\frac{3}{4}.

$$\frac{1}{3}x+\frac{1}{4}=\frac{2}{5}x+\frac{2}{5}\left(-\frac{3}{4}\right)$$

Multiply \frac{2}{5} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}x+\frac{1}{4}=\frac{2}{5}x+\frac{2\left(-3\right)}{5\times 4}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 4}.

$$\frac{1}{3}x+\frac{1}{4}=\frac{2}{5}x+\frac{-6}{20}$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

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

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

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

Combine \frac{1}{3}x and -\frac{2}{5}x to get -\frac{1}{15}x.

$$-\frac{1}{15}x+\frac{1}{4}=-\frac{3}{10}$$

Subtract \frac{1}{4} from both sides.

$$-\frac{1}{15}x=-\frac{3}{10}-\frac{1}{4}$$

Least common multiple of 10 and 4 is 20. Convert -\frac{3}{10} and \frac{1}{4} to fractions with denominator 20.

$$-\frac{1}{15}x=-\frac{6}{20}-\frac{5}{20}$$

Since -\frac{6}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}x=\frac{-6-5}{20}$$

Subtract 5 from -6 to get -11.

$$-\frac{1}{15}x=-\frac{11}{20}$$

Multiply both sides by -15, the reciprocal of -\frac{1}{15}.

$$x=-\frac{11}{20}\left(-15\right)$$

Express -\frac{11}{20}\left(-15\right) as a single fraction.

$$x=\frac{-11\left(-15\right)}{20}$$

Multiply -11 and -15 to get 165.

$$x=\frac{165}{20}$$

Reduce the fraction \frac{165}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{33}{4}$$