Solve 3/4x+2/5=133/120

$$\frac{ 3 }{ 4 } x+ \frac{ 2 }{ 5 } = \frac{ 133 }{ 120 }$$

Solve for x

$$x=\frac{17}{18}\approx 0.944444444$$

Steps for Solving Linear Equation

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

$$\frac{3}{4}x=\frac{133}{120}-\frac{2}{5}$$

Least common multiple of 120 and 5 is 120. Convert \frac{133}{120} and \frac{2}{5} to fractions with denominator 120.

$$\frac{3}{4}x=\frac{133}{120}-\frac{48}{120}$$

Since \frac{133}{120} and \frac{48}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}x=\frac{133-48}{120}$$

Subtract 48 from 133 to get 85.

$$\frac{3}{4}x=\frac{85}{120}$$

Reduce the fraction \frac{85}{120} to lowest terms by extracting and canceling out 5.

$$\frac{3}{4}x=\frac{17}{24}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$x=\frac{17}{24}\times \frac{4}{3}$$

Multiply \frac{17}{24} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{17\times 4}{24\times 3}$$

Do the multiplications in the fraction \frac{17\times 4}{24\times 3}.

$$x=\frac{68}{72}$$

Reduce the fraction \frac{68}{72} to lowest terms by extracting and canceling out 4.

$$x=\frac{17}{18}$$