Solve 1/4(p-7)=1/6(p-3)

$$\frac { 1 } { 4 } ( p - 7 ) = \frac { 1 } { 6 } ( p - 3 )$$

Solve for p

$$p=15$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by p-7.

$$\frac{1}{4}p+\frac{1}{4}\left(-7\right)=\frac{1}{6}\left(p-3\right)$$

Multiply \frac{1}{4} and -7 to get \frac{-7}{4}.

$$\frac{1}{4}p+\frac{-7}{4}=\frac{1}{6}\left(p-3\right)$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$\frac{1}{4}p-\frac{7}{4}=\frac{1}{6}\left(p-3\right)$$

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

$$\frac{1}{4}p-\frac{7}{4}=\frac{1}{6}p+\frac{1}{6}\left(-3\right)$$

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

$$\frac{1}{4}p-\frac{7}{4}=\frac{1}{6}p+\frac{-3}{6}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}p-\frac{7}{4}=\frac{1}{6}p-\frac{1}{2}$$

Subtract \frac{1}{6}p from both sides.

$$\frac{1}{4}p-\frac{7}{4}-\frac{1}{6}p=-\frac{1}{2}$$

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

$$\frac{1}{12}p-\frac{7}{4}=-\frac{1}{2}$$

Add \frac{7}{4} to both sides.

$$\frac{1}{12}p=-\frac{1}{2}+\frac{7}{4}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{1}{12}p=-\frac{2}{4}+\frac{7}{4}$$

Since -\frac{2}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}p=\frac{-2+7}{4}$$

Add -2 and 7 to get 5.

$$\frac{1}{12}p=\frac{5}{4}$$

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

$$p=\frac{5}{4}\times 12$$

Express \frac{5}{4}\times 12 as a single fraction.

$$p=\frac{5\times 12}{4}$$

Multiply 5 and 12 to get 60.

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

Divide 60 by 4 to get 15.

$$p=15$$