Solve 3x-1/4=2x+1/3-5/6

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

Solve for x

$$x=-\frac{1}{4}=-0.25$$

Steps for Solving Linear Equation

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 2 to get -3.

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

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

Subtract 2x from both sides.

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

Combine 3x and -2x to get x.

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

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

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

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

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

Since -\frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add -2 and 1 to get -1.

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