Algebra Examples

$\frac{3 p - 1}{24} - \frac{2 p + 6}{36} - 1 = 0$

Step 1

Simplify $\frac{3 p - 1}{24} - \frac{2 p + 6}{36} - 1$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{3 p - 1}{24}$ by $\frac{3}{3}$ .

$\frac{3 p - 1}{24} \cdot \frac{3}{3} - \frac{2 p + 6}{36} - 1 = 0$

Step 1.1.2

Multiply $\frac{3 p - 1}{24}$ by $\frac{3}{3}$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - \frac{2 p + 6}{36} - 1 = 0$

Step 1.1.3

Multiply $\frac{2 p + 6}{36}$ by $\frac{2}{2}$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - (\frac{2 p + 6}{36} \cdot \frac{2}{2}) - 1 = 0$

Step 1.1.4

Multiply $\frac{2 p + 6}{36}$ by $\frac{2}{2}$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} - 1 = 0$

Step 1.1.5

Write $- 1$ as a fraction with denominator $1$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} + \frac{- 1}{1} = 0$

Step 1.1.6

Multiply $\frac{- 1}{1}$ by $\frac{72}{72}$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} + \frac{- 1}{1} \cdot \frac{72}{72} = 0$

Step 1.1.7

Multiply $\frac{- 1}{1}$ by $\frac{72}{72}$ .

$\frac{(3 p - 1) \cdot 3}{24 \cdot 3} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} + \frac{- 1 \cdot 72}{72} = 0$

Step 1.1.8

Reorder the factors of $24 \cdot 3$ .

$\frac{(3 p - 1) \cdot 3}{3 \cdot 24} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} + \frac{- 1 \cdot 72}{72} = 0$

Step 1.1.9

Multiply $3$ by $24$ .

$\frac{(3 p - 1) \cdot 3}{72} - \frac{(2 p + 6) \cdot 2}{36 \cdot 2} + \frac{- 1 \cdot 72}{72} = 0$

Step 1.1.10

Reorder the factors of $36 \cdot 2$ .

$\frac{(3 p - 1) \cdot 3}{72} - \frac{(2 p + 6) \cdot 2}{2 \cdot 36} + \frac{- 1 \cdot 72}{72} = 0$

Step 1.1.11

Multiply $2$ by $36$ .

$\frac{(3 p - 1) \cdot 3}{72} - \frac{(2 p + 6) \cdot 2}{72} + \frac{- 1 \cdot 72}{72} = 0$

Step 1.2

Combine the numerators over the common denominator.

$\frac{(3 p - 1) \cdot 3 - (2 p + 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{3 p \cdot 3 - 1 \cdot 3 - (2 p + 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{9 p - 1 \cdot 3 - (2 p + 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.3

Multiply $- 1$ by $3$ .

$\frac{9 p - 3 - (2 p + 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.4

Apply the distributive property.

$\frac{9 p - 3 + (- (2 p) - 1 \cdot 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.5

Multiply $2$ by $- 1$ .

$\frac{9 p - 3 + (- 2 p - 1 \cdot 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.6

Multiply $- 1$ by $6$ .

$\frac{9 p - 3 + (- 2 p - 6) \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.7

Apply the distributive property.

$\frac{9 p - 3 - 2 p \cdot 2 - 6 \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.8

Multiply $2$ by $- 2$ .

$\frac{9 p - 3 - 4 p - 6 \cdot 2 - 1 \cdot 72}{72} = 0$

Step 1.3.9

Multiply $- 6$ by $2$ .

$\frac{9 p - 3 - 4 p - 12 - 1 \cdot 72}{72} = 0$

Step 1.3.10

Multiply $- 1$ by $72$ .

$\frac{9 p - 3 - 4 p - 12 - 72}{72} = 0$

Step 1.4

Simplify by adding terms.

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Step 1.4.1

Subtract $4 p$ from $9 p$ .

$\frac{5 p - 3 - 12 - 72}{72} = 0$

Step 1.4.2

Simplify by subtracting numbers.

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Step 1.4.2.1

Subtract $12$ from $- 3$ .

$\frac{5 p - 15 - 72}{72} = 0$

Step 1.4.2.2

Subtract $72$ from $- 15$ .

$\frac{5 p - 87}{72} = 0$

Step 2

Set the numerator equal to zero.

$5 p - 87 = 0$

Step 3

Solve the equation for $p$ .

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Step 3.1

Add $87$ to both sides of the equation.

$5 p = 87$

Step 3.2

Divide each term in $5 p = 87$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 p = 87$ by $5$ .

$\frac{5 p}{5} = \frac{87}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 p}{5} = \frac{87}{5}$

Step 3.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{87}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$p = \frac{87}{5}$

Decimal Form:

$p = 17.4$

Mixed Number Form:

$p = 17 \frac{2}{5}$