Solve 3/4x-1/6=1/5

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

Solve for x

$$x=\frac{22}{45}\approx 0.488888889$$

Steps for Solving Linear Equation

Add \frac{1}{6} to both sides.

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

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{3}{4}x=\frac{6}{30}+\frac{5}{30}$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}x=\frac{6+5}{30}$$

Add 6 and 5 to get 11.

$$\frac{3}{4}x=\frac{11}{30}$$

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

$$x=\frac{11}{30}\times \frac{4}{3}$$

Multiply \frac{11}{30} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\times 4}{30\times 3}$$

Do the multiplications in the fraction \frac{11\times 4}{30\times 3}.

$$x=\frac{44}{90}$$

Reduce the fraction \frac{44}{90} to lowest terms by extracting and canceling out 2.

$$x=\frac{22}{45}$$