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

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 4x-1.

$$\frac{1}{2}\times 4x+\frac{1}{2}\left(-1\right)+\frac{1}{3}\left(6x-2\right)=-\frac{1}{6}$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x+\frac{1}{2}\left(-1\right)+\frac{1}{3}\left(6x-2\right)=-\frac{1}{6}$$

Divide 4 by 2 to get 2.

$$2x+\frac{1}{2}\left(-1\right)+\frac{1}{3}\left(6x-2\right)=-\frac{1}{6}$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$2x-\frac{1}{2}+\frac{1}{3}\left(6x-2\right)=-\frac{1}{6}$$

Use the distributive property to multiply \frac{1}{3} by 6x-2.

$$2x-\frac{1}{2}+\frac{1}{3}\times 6x+\frac{1}{3}\left(-2\right)=-\frac{1}{6}$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$2x-\frac{1}{2}+\frac{6}{3}x+\frac{1}{3}\left(-2\right)=-\frac{1}{6}$$

Divide 6 by 3 to get 2.

$$2x-\frac{1}{2}+2x+\frac{1}{3}\left(-2\right)=-\frac{1}{6}$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Combine 2x and 2x to get 4x.

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

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

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

Since -\frac{3}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from -3 to get -7.

$$4x-\frac{7}{6}=-\frac{1}{6}$$

Add \frac{7}{6} to both sides.

$$4x=-\frac{1}{6}+\frac{7}{6}$$

Since -\frac{1}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$4x=\frac{-1+7}{6}$$

Add -1 and 7 to get 6.

$$4x=\frac{6}{6}$$

Divide 6 by 6 to get 1.

$$4x=1$$

Divide both sides by 4.

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