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

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

Solve for x

$$x=-9$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Convert 2 to fraction \frac{8}{4}.

$$\frac{1}{4}x-\frac{3}{4}+\frac{8}{4}=\frac{1}{3}\left(x+6\right)$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}x+\frac{-3+8}{4}=\frac{1}{3}\left(x+6\right)$$

Add -3 and 8 to get 5.

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

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

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

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

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

Divide 6 by 3 to get 2.

$$\frac{1}{4}x+\frac{5}{4}=\frac{1}{3}x+2$$

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

$$\frac{1}{4}x+\frac{5}{4}-\frac{1}{3}x=2$$

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

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

Subtract \frac{5}{4} from both sides.

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

Convert 2 to fraction \frac{8}{4}.

$$-\frac{1}{12}x=\frac{8}{4}-\frac{5}{4}$$

Since \frac{8}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{12}x=\frac{8-5}{4}$$

Subtract 5 from 8 to get 3.

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

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

$$x=\frac{3}{4}\left(-12\right)$$

Express \frac{3}{4}\left(-12\right) as a single fraction.

$$x=\frac{3\left(-12\right)}{4}$$

Multiply 3 and -12 to get -36.

$$x=\frac{-36}{4}$$

Divide -36 by 4 to get -9.

$$x=-9$$