Algebra Examples

$\frac{3}{10} p = \frac{1}{2} + \frac{2}{5} p + 1 \frac{1}{10}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{3}{10}$ and $p$ .

$\frac{3 p}{10} = \frac{1}{2} + \frac{2}{5} p + 1 \frac{1}{10}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{1}{2} + \frac{2}{5} p + 1 \frac{1}{10}$ .

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Step 2.1.1

Convert $1 \frac{1}{10}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{3 p}{10} = \frac{1}{2} + \frac{2}{5} p + 1 + \frac{1}{10}$

Step 2.1.1.2

Add $1$ and $\frac{1}{10}$ .

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Step 2.1.1.2.1

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

$\frac{3 p}{10} = \frac{1}{2} + \frac{2}{5} p + \frac{10}{10} + \frac{1}{10}$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{3 p}{10} = \frac{1}{2} + \frac{2}{5} p + \frac{10 + 1}{10}$

Step 2.1.1.2.3

Add $10$ and $1$ .

$\frac{3 p}{10} = \frac{1}{2} + \frac{2}{5} p + \frac{11}{10}$

Step 2.1.2

Combine $\frac{2}{5}$ and $p$ .

$\frac{3 p}{10} = \frac{1}{2} + \frac{2 p}{5} + \frac{11}{10}$

Step 2.1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{1}{2} \cdot \frac{5}{5} + \frac{11}{10}$

Step 2.1.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{5}{2 \cdot 5} + \frac{11}{10}$

Step 2.1.4.2

Multiply $2$ by $5$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{5}{10} + \frac{11}{10}$

Step 2.1.5

Simplify the expression.

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Step 2.1.5.1

Combine the numerators over the common denominator.

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{5 + 11}{10}$

Step 2.1.5.2

Add $5$ and $11$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{16}{10}$

Step 2.1.6

Cancel the common factor of $16$ and $10$ .

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Step 2.1.6.1

Factor $2$ out of $16$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{2 (8)}{10}$

Step 2.1.6.2

Cancel the common factors.

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Step 2.1.6.2.1

Factor $2$ out of $10$ .

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{2 \cdot 8}{2 \cdot 5}$

Step 2.1.6.2.2

Cancel the common factor.

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{2 \cdot 8}{2 \cdot 5}$

Step 2.1.6.2.3

Rewrite the expression.

$\frac{3 p}{10} = \frac{2 p}{5} + \frac{8}{5}$

Step 3

Multiply both sides by $10$ .

$\frac{3 p}{10} \cdot 10 = (\frac{2 p}{5} + \frac{8}{5}) \cdot 10$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{3 p}{10} \cdot 10 = (\frac{2 p}{5} + \frac{8}{5}) \cdot 10$

Step 4.1.1.2

Rewrite the expression.

$3 p = (\frac{2 p}{5} + \frac{8}{5}) \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $(\frac{2 p}{5} + \frac{8}{5}) \cdot 10$ .

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Step 4.2.1.1

Apply the distributive property.

$3 p = \frac{2 p}{5} \cdot 10 + \frac{8}{5} \cdot 10$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Factor $5$ out of $10$ .

$3 p = \frac{2 p}{5} \cdot (5 (2)) + \frac{8}{5} \cdot 10$

Step 4.2.1.2.2

Cancel the common factor.

$3 p = \frac{2 p}{5} \cdot (5 \cdot 2) + \frac{8}{5} \cdot 10$

Step 4.2.1.2.3

Rewrite the expression.

$3 p = 2 p \cdot 2 + \frac{8}{5} \cdot 10$

Step 4.2.1.3

Multiply $2$ by $2$ .

$3 p = 4 p + \frac{8}{5} \cdot 10$

Step 4.2.1.4

Cancel the common factor of $5$ .

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Step 4.2.1.4.1

Factor $5$ out of $10$ .

$3 p = 4 p + \frac{8}{5} \cdot (5 (2))$

Step 4.2.1.4.2

Cancel the common factor.

$3 p = 4 p + \frac{8}{5} \cdot (5 \cdot 2)$

Step 4.2.1.4.3

Rewrite the expression.

$3 p = 4 p + 8 \cdot 2$

Step 4.2.1.5

Multiply $8$ by $2$ .

$3 p = 4 p + 16$

Step 5

Solve for $p$ .

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Step 5.1

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

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Step 5.1.1

Subtract $4 p$ from both sides of the equation.

$3 p - 4 p = 16$

Step 5.1.2

Subtract $4 p$ from $3 p$ .

$- p = 16$

Step 5.2

Divide each term in $- p = 16$ by $- 1$ and simplify.

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Step 5.2.1

Divide each term in $- p = 16$ by $- 1$ .

$\frac{- p}{- 1} = \frac{16}{- 1}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Dividing two negative values results in a positive value.

$\frac{p}{1} = \frac{16}{- 1}$

Step 5.2.2.2

Divide $p$ by $1$ .

$p = \frac{16}{- 1}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $16$ by $- 1$ .

$p = - 16$