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

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

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

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

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

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

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

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

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

Divide 6 by 3 to get 2.

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{4}x and -\frac{2}{3}x to get -\frac{5}{12}x.

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

Add \frac{1}{2} to both sides.

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

Convert 2 to fraction \frac{4}{2}.

$$-\frac{5}{12}x=\frac{4}{2}+\frac{1}{2}$$

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

$$-\frac{5}{12}x=\frac{4+1}{2}$$

Add 4 and 1 to get 5.

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

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

$$x=\frac{5}{2}\left(-\frac{12}{5}\right)$$

Multiply \frac{5}{2} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\left(-12\right)}{2\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$x=-6$$