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

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

Solve for x

$$x=32$$

Steps for Solving Linear Equation

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

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

Multiply -2 and \frac{1}{6} to get \frac{-2}{6}.

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

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

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

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

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

Since -\frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add -1 and 6 to get 5.

$$x\times \frac{1}{6}+\frac{5}{3}=\left(x-4\right)\times \frac{1}{4}$$

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

$$x\times \frac{1}{6}+\frac{5}{3}=x\times \frac{1}{4}-4\times \frac{1}{4}$$

Multiply -4 times \frac{1}{4}.

$$x\times \frac{1}{6}+\frac{5}{3}=x\times \frac{1}{4}-1$$

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

$$x\times \frac{1}{6}+\frac{5}{3}-x\times \frac{1}{4}=-1$$

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

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

Subtract \frac{5}{3} from both sides.

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

Convert -1 to fraction -\frac{3}{3}.

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

Since -\frac{3}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from -3 to get -8.

$$-\frac{1}{12}x=-\frac{8}{3}$$

Multiply both sides by -12, the reciprocal of -\frac{1}{12}.

$$x=-\frac{8}{3}\left(-12\right)$$

Express -\frac{8}{3}\left(-12\right) as a single fraction.

$$x=\frac{-8\left(-12\right)}{3}$$

Multiply -8 and -12 to get 96.

$$x=\frac{96}{3}$$

Divide 96 by 3 to get 32.

$$x=32$$