Solve 1/4+1/12x=1/3x-1/2

$$\frac{ 1 }{ 4 } + \frac{ 1 }{ 12 } x= \frac{ 1 }{ 3 } x- \frac{ 1 }{ 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}x from both sides.

$$\frac{1}{4}+\frac{1}{12}x-\frac{1}{3}x=-\frac{1}{2}$$

Combine \frac{1}{12}x and -\frac{1}{3}x to get -\frac{1}{4}x.

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

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

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

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

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

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

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

Subtract 1 from -2 to get -3.

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

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=-\frac{3}{4}\left(-4\right)$$

Express -\frac{3}{4}\left(-4\right) as a single fraction.

$$x=\frac{-3\left(-4\right)}{4}$$

Multiply -3 and -4 to get 12.

$$x=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x=3$$