Solve 1/2x-1/4=1/6x+1/3

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

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Subtract \frac{1}{6}x from both sides.

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

Combine \frac{1}{2}x and -\frac{1}{6}x to get \frac{1}{3}x.

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

Add \frac{1}{4} to both sides.

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

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{3}x=\frac{4}{12}+\frac{3}{12}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x=\frac{4+3}{12}$$

Add 4 and 3 to get 7.

$$\frac{1}{3}x=\frac{7}{12}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$x=\frac{7}{12}\times 3$$

Express \frac{7}{12}\times 3 as a single fraction.

$$x=\frac{7\times 3}{12}$$

Multiply 7 and 3 to get 21.

$$x=\frac{21}{12}$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{7}{4}$$