Basic Math Examples

$\frac{1}{2} \cdot (p + 6) = \frac{7}{2} \cdot (3 - p)$

Step 1

Simplify $\frac{1}{2} \cdot (p + 6)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (p + 6) = \frac{7}{2} \cdot (3 - p)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (p + 6) = \frac{7}{2} \cdot (3 - p)$

Step 1.3

Apply the distributive property.

$\frac{1}{2} p + \frac{1}{2} \cdot 6 = \frac{7}{2} \cdot (3 - p)$

Step 1.4

Combine $\frac{1}{2}$ and $p$ .

$\frac{p}{2} + \frac{1}{2} \cdot 6 = \frac{7}{2} \cdot (3 - p)$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $6$ .

$\frac{p}{2} + \frac{1}{2} \cdot (2 (3)) = \frac{7}{2} \cdot (3 - p)$

Step 1.5.2

Cancel the common factor.

$\frac{p}{2} + \frac{1}{2} \cdot (2 \cdot 3) = \frac{7}{2} \cdot (3 - p)$

Step 1.5.3

Rewrite the expression.

$\frac{p}{2} + 3 = \frac{7}{2} \cdot (3 - p)$

Step 2

Simplify $\frac{7}{2} \cdot (3 - p)$ .

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Step 2.1

Apply the distributive property.

$\frac{p}{2} + 3 = \frac{7}{2} \cdot 3 + \frac{7}{2} (- p)$

Step 2.2

Multiply $\frac{7}{2} \cdot 3$ .

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Step 2.2.1

Combine $\frac{7}{2}$ and $3$ .

$\frac{p}{2} + 3 = \frac{7 \cdot 3}{2} + \frac{7}{2} (- p)$

Step 2.2.2

Multiply $7$ by $3$ .

$\frac{p}{2} + 3 = \frac{21}{2} + \frac{7}{2} (- p)$

Step 2.3

Combine $\frac{7}{2}$ and $p$ .

$\frac{p}{2} + 3 = \frac{21}{2} - \frac{7 p}{2}$

Step 3

Move all terms containing $p$ to the left side of the equation.

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Step 3.1

Add $\frac{7 p}{2}$ to both sides of the equation.

$\frac{p}{2} + 3 + \frac{7 p}{2} = \frac{21}{2}$

Step 3.2

Combine the numerators over the common denominator.

$3 + \frac{p + 7 p}{2} = \frac{21}{2}$

Step 3.3

Add $p$ and $7 p$ .

$3 + \frac{8 p}{2} = \frac{21}{2}$

Step 3.4

Cancel the common factor of $8$ and $2$ .

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Step 3.4.1

Factor $2$ out of $8 p$ .

$3 + \frac{2 (4 p)}{2} = \frac{21}{2}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $2$ .

$3 + \frac{2 (4 p)}{2 (1)} = \frac{21}{2}$

Step 3.4.2.2

Cancel the common factor.

$3 + \frac{2 (4 p)}{2 \cdot 1} = \frac{21}{2}$

Step 3.4.2.3

Rewrite the expression.

$3 + \frac{4 p}{1} = \frac{21}{2}$

Step 3.4.2.4

Divide $4 p$ by $1$ .

$3 + 4 p = \frac{21}{2}$

Step 4

Move all terms not containing $p$ to the right side of the equation.

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Step 4.1

Subtract $3$ from both sides of the equation.

$4 p = \frac{21}{2} - 3$

Step 4.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 p = \frac{21}{2} - 3 \cdot \frac{2}{2}$

Step 4.3

Combine $- 3$ and $\frac{2}{2}$ .

$4 p = \frac{21}{2} + \frac{- 3 \cdot 2}{2}$

Step 4.4

Combine the numerators over the common denominator.

$4 p = \frac{21 - 3 \cdot 2}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $2$ .

$4 p = \frac{21 - 6}{2}$

Step 4.5.2

Subtract $6$ from $21$ .

$4 p = \frac{15}{2}$

Step 5

Divide each term in $4 p = \frac{15}{2}$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 p = \frac{15}{2}$ by $4$ .

$\frac{4 p}{4} = \frac{\frac{15}{2}}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 p}{4} = \frac{\frac{15}{2}}{4}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{\frac{15}{2}}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$p = \frac{15}{2} \cdot \frac{1}{4}$

Step 5.3.2

Multiply $\frac{15}{2} \cdot \frac{1}{4}$ .

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Step 5.3.2.1

Multiply $\frac{15}{2}$ by $\frac{1}{4}$ .

$p = \frac{15}{2 \cdot 4}$

Step 5.3.2.2

Multiply $2$ by $4$ .

$p = \frac{15}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{15}{8}$

Decimal Form:

$p = 1.875$

Mixed Number Form:

$p = 1 \frac{7}{8}$