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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x-3.

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

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

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

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

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

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

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

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

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

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

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

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

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

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

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

Add \frac{3}{4} to both sides.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{1}{12}x=-\frac{8}{12}+\frac{9}{12}$$

Since -\frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$-\frac{1}{12}x=\frac{-8+9}{12}$$

Add -8 and 9 to get 1.

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

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

$$x=\frac{1}{12}\left(-12\right)$$

Multiply \frac{1}{12} and -12 to get \frac{-12}{12}.

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

Divide -12 by 12 to get -1.

$$x=-1$$