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

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

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

Subtract \frac{3}{4}x from both sides.

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

Combine \frac{1}{12}x and -\frac{3}{4}x to get -\frac{2}{3}x.

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

Add \frac{2}{3} to both sides.

$$-\frac{2}{3}x=2+\frac{2}{3}$$

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

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

Add 6 and 2 to get 8.

$$-\frac{2}{3}x=\frac{8}{3}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x=\frac{8}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{8}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{8\left(-3\right)}{3\times 2}.

$$x=\frac{-24}{6}$$

Divide -24 by 6 to get -4.

$$x=-4$$