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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

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

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

Combine \frac{1}{4}x and \frac{1}{6}x to get \frac{5}{12}x.

$$\frac{5}{12}x+\frac{1}{3}=-\frac{1}{2}$$

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

$$\frac{5}{12}x=-\frac{1}{2}-\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{5}{12}x=-\frac{3}{6}-\frac{2}{6}$$

Since -\frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{12}x=\frac{-3-2}{6}$$

Subtract 2 from -3 to get -5.

$$\frac{5}{12}x=-\frac{5}{6}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=-\frac{5}{6}\times \frac{12}{5}$$

Multiply -\frac{5}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 12}{6\times 5}$$

Do the multiplications in the fraction \frac{-5\times 12}{6\times 5}.

$$x=\frac{-60}{30}$$

Divide -60 by 30 to get -2.

$$x=-2$$