Pre-Algebra Examples

$\frac{4 p + 8}{24} - \frac{2 p - 9}{6} - \frac{p + 3}{18} = 0$

Step 1

Simplify $\frac{4 p + 8}{24} - \frac{2 p - 9}{6} - \frac{p + 3}{18}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{4 p + 8}{24}$ by $\frac{3}{3}$ .

$\frac{4 p + 8}{24} \cdot \frac{3}{3} - \frac{2 p - 9}{6} - \frac{p + 3}{18} = 0$

Step 1.1.2

Multiply $\frac{4 p + 8}{24}$ by $\frac{3}{3}$ .

$\frac{(4 p + 8) \cdot 3}{24 \cdot 3} - \frac{2 p - 9}{6} - \frac{p + 3}{18} = 0$

Step 1.1.3

Multiply $\frac{2 p - 9}{6}$ by $\frac{12}{12}$ .

$\frac{(4 p + 8) \cdot 3}{24 \cdot 3} - (\frac{2 p - 9}{6} \cdot \frac{12}{12}) - \frac{p + 3}{18} = 0$

Step 1.1.4

Multiply $\frac{2 p - 9}{6}$ by $\frac{12}{12}$ .

$\frac{(4 p + 8) \cdot 3}{24 \cdot 3} - \frac{(2 p - 9) \cdot 12}{6 \cdot 12} - \frac{p + 3}{18} = 0$

Step 1.1.5

Multiply $\frac{p + 3}{18}$ by $\frac{4}{4}$ .

$\frac{(4 p + 8) \cdot 3}{24 \cdot 3} - \frac{(2 p - 9) \cdot 12}{6 \cdot 12} - (\frac{p + 3}{18} \cdot \frac{4}{4}) = 0$

Step 1.1.6

Multiply $\frac{p + 3}{18}$ by $\frac{4}{4}$ .

$\frac{(4 p + 8) \cdot 3}{24 \cdot 3} - \frac{(2 p - 9) \cdot 12}{6 \cdot 12} - \frac{(p + 3) \cdot 4}{18 \cdot 4} = 0$

Step 1.1.7

Reorder the factors of $24 \cdot 3$ .

$\frac{(4 p + 8) \cdot 3}{3 \cdot 24} - \frac{(2 p - 9) \cdot 12}{6 \cdot 12} - \frac{(p + 3) \cdot 4}{18 \cdot 4} = 0$

Step 1.1.8

Multiply $3$ by $24$ .

$\frac{(4 p + 8) \cdot 3}{72} - \frac{(2 p - 9) \cdot 12}{6 \cdot 12} - \frac{(p + 3) \cdot 4}{18 \cdot 4} = 0$

Step 1.1.9

Multiply $6$ by $12$ .

$\frac{(4 p + 8) \cdot 3}{72} - \frac{(2 p - 9) \cdot 12}{72} - \frac{(p + 3) \cdot 4}{18 \cdot 4} = 0$

Step 1.1.10

Reorder the factors of $18 \cdot 4$ .

$\frac{(4 p + 8) \cdot 3}{72} - \frac{(2 p - 9) \cdot 12}{72} - \frac{(p + 3) \cdot 4}{4 \cdot 18} = 0$

Step 1.1.11

Multiply $4$ by $18$ .

$\frac{(4 p + 8) \cdot 3}{72} - \frac{(2 p - 9) \cdot 12}{72} - \frac{(p + 3) \cdot 4}{72} = 0$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(4 p + 8) \cdot 3 - (2 p - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{4 p \cdot 3 + 8 \cdot 3 - (2 p - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{12 p + 8 \cdot 3 - (2 p - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.3

Multiply $8$ by $3$ .

$\frac{12 p + 24 - (2 p - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.4

Apply the distributive property.

$\frac{12 p + 24 + (- (2 p) - - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.5

Multiply $2$ by $- 1$ .

$\frac{12 p + 24 + (- 2 p - - 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.6

Multiply $- 1$ by $- 9$ .

$\frac{12 p + 24 + (- 2 p + 9) \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.7

Apply the distributive property.

$\frac{12 p + 24 - 2 p \cdot 12 + 9 \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.8

Multiply $12$ by $- 2$ .

$\frac{12 p + 24 - 24 p + 9 \cdot 12 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.9

Multiply $9$ by $12$ .

$\frac{12 p + 24 - 24 p + 108 - (p + 3) \cdot 4}{72} = 0$

Step 1.3.10

Apply the distributive property.

$\frac{12 p + 24 - 24 p + 108 + (- p - 1 \cdot 3) \cdot 4}{72} = 0$

Step 1.3.11

Multiply $- 1$ by $3$ .

$\frac{12 p + 24 - 24 p + 108 + (- p - 3) \cdot 4}{72} = 0$

Step 1.3.12

Apply the distributive property.

$\frac{12 p + 24 - 24 p + 108 - p \cdot 4 - 3 \cdot 4}{72} = 0$

Step 1.3.13

Multiply $4$ by $- 1$ .

$\frac{12 p + 24 - 24 p + 108 - 4 p - 3 \cdot 4}{72} = 0$

Step 1.3.14

Multiply $- 3$ by $4$ .

$\frac{12 p + 24 - 24 p + 108 - 4 p - 12}{72} = 0$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $24 p$ from $12 p$ .

$\frac{- 12 p + 24 + 108 - 4 p - 12}{72} = 0$

Step 1.4.2

Subtract $4 p$ from $- 12 p$ .

$\frac{- 16 p + 24 + 108 - 12}{72} = 0$

Step 1.4.3

Simplify by adding and subtracting.

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Step 1.4.3.1

Add $24$ and $108$ .

$\frac{- 16 p + 132 - 12}{72} = 0$

Step 1.4.3.2

Subtract $12$ from $132$ .

$\frac{- 16 p + 120}{72} = 0$

Step 1.4.4

Cancel the common factor of $- 16 p + 120$ and $72$ .

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Step 1.4.4.1

Factor $8$ out of $- 16 p$ .

$\frac{8 (- 2 p) + 120}{72} = 0$

Step 1.4.4.2

Factor $8$ out of $120$ .

$\frac{8 (- 2 p) + 8 (15)}{72} = 0$

Step 1.4.4.3

Factor $8$ out of $8 (- 2 p) + 8 (15)$ .

$\frac{8 (- 2 p + 15)}{72} = 0$

Step 1.4.4.4

Cancel the common factors.

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Step 1.4.4.4.1

Factor $8$ out of $72$ .

$\frac{8 (- 2 p + 15)}{8 (9)} = 0$

Step 1.4.4.4.2

Cancel the common factor.

$\frac{8 (- 2 p + 15)}{8 \cdot 9} = 0$

Step 1.4.4.4.3

Rewrite the expression.

$\frac{- 2 p + 15}{9} = 0$

Step 1.4.5

Factor $- 1$ out of $- 2 p$ .

$\frac{- (2 p) + 15}{9} = 0$

Step 1.4.6

Rewrite $15$ as $- 1 (- 15)$ .

$\frac{- (2 p) - 1 (- 15)}{9} = 0$

Step 1.4.7

Factor $- 1$ out of $- (2 p) - 1 (- 15)$ .

$\frac{- (2 p - 15)}{9} = 0$

Step 1.4.8

Simplify the expression.

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Step 1.4.8.1

Rewrite $- (2 p - 15)$ as $- 1 (2 p - 15)$ .

$\frac{- 1 (2 p - 15)}{9} = 0$

Step 1.4.8.2

Move the negative in front of the fraction.

$- \frac{2 p - 15}{9} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$p = \frac{15}{2}$

Step 3