Solve 1/4(a-3)=1/3(a-6)

$$\frac { 1 } { 4 } ( a - 3 ) = \frac { 1 } { 3 } ( a - 6 )$$

Solve for a

$$a=15$$

Steps for Solving Linear Equation

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

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

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

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

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

$$\frac{1}{4}a-\frac{3}{4}=\frac{1}{3}\left(a-6\right)$$

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

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

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

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

Divide -6 by 3 to get -2.

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

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

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

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

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

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

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

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

$$-\frac{1}{12}a=-\frac{8}{4}+\frac{3}{4}$$

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

$$-\frac{1}{12}a=\frac{-8+3}{4}$$

Add -8 and 3 to get -5.

$$-\frac{1}{12}a=-\frac{5}{4}$$

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

$$a=-\frac{5}{4}\left(-12\right)$$

Express -\frac{5}{4}\left(-12\right) as a single fraction.

$$a=\frac{-5\left(-12\right)}{4}$$

Multiply -5 and -12 to get 60.

$$a=\frac{60}{4}$$

Divide 60 by 4 to get 15.

$$a=15$$