Algebra Examples

$\frac{4}{5} p + 6 = - \frac{1}{3} p - 3$

Step 1

Combine $\frac{4}{5}$ and $p$ .

$\frac{4 p}{5} + 6 = - \frac{1}{3} p - 3$

Step 2

Combine $p$ and $\frac{1}{3}$ .

$\frac{4 p}{5} + 6 = - \frac{p}{3} - 3$

Step 3

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

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Step 3.1

Add $\frac{p}{3}$ to both sides of the equation.

$\frac{4 p}{5} + 6 + \frac{p}{3} = - 3$

Step 3.2

To write $\frac{4 p}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 p}{5} \cdot \frac{3}{3} + \frac{p}{3} + 6 = - 3$

Step 3.3

To write $\frac{p}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 p}{5} \cdot \frac{3}{3} + \frac{p}{3} \cdot \frac{5}{5} + 6 = - 3$

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{4 p}{5}$ by $\frac{3}{3}$ .

$\frac{4 p \cdot 3}{5 \cdot 3} + \frac{p}{3} \cdot \frac{5}{5} + 6 = - 3$

Step 3.4.2

Multiply $5$ by $3$ .

$\frac{4 p \cdot 3}{15} + \frac{p}{3} \cdot \frac{5}{5} + 6 = - 3$

Step 3.4.3

Multiply $\frac{p}{3}$ by $\frac{5}{5}$ .

$\frac{4 p \cdot 3}{15} + \frac{p \cdot 5}{3 \cdot 5} + 6 = - 3$

Step 3.4.4

Multiply $3$ by $5$ .

$\frac{4 p \cdot 3}{15} + \frac{p \cdot 5}{15} + 6 = - 3$

Step 3.5

Combine the numerators over the common denominator.

$\frac{4 p \cdot 3 + p \cdot 5}{15} + 6 = - 3$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $p$ out of $4 p \cdot 3 + p \cdot 5$ .

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Step 3.6.1.1.1

Factor $p$ out of $4 p \cdot 3$ .

$\frac{p (4 \cdot 3) + p \cdot 5}{15} + 6 = - 3$

Step 3.6.1.1.2

Factor $p$ out of $p \cdot 5$ .

$\frac{p (4 \cdot 3) + p (5)}{15} + 6 = - 3$

Step 3.6.1.1.3

Factor $p$ out of $p (4 \cdot 3) + p (5)$ .

$\frac{p (4 \cdot 3 + 5)}{15} + 6 = - 3$

Step 3.6.1.2

Multiply $4$ by $3$ .

$\frac{p (12 + 5)}{15} + 6 = - 3$

Step 3.6.1.3

Add $12$ and $5$ .

$\frac{p \cdot 17}{15} + 6 = - 3$

Step 3.6.2

Move $17$ to the left of $p$ .

$\frac{17 p}{15} + 6 = - 3$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$\frac{17 p}{15} = - 3 - 6$

Step 4.2

Subtract $6$ from $- 3$ .

$\frac{17 p}{15} = - 9$

Step 5

Multiply both sides of the equation by $\frac{15}{17}$ .

$\frac{15}{17} \cdot \frac{17 p}{15} = \frac{15}{17} \cdot - 9$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{15}{17} \cdot \frac{17 p}{15}$ .

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Step 6.1.1.1

Cancel the common factor of $15$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{15}{17} \cdot \frac{17 p}{15} = \frac{15}{17} \cdot - 9$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{17} (17 p) = \frac{15}{17} \cdot - 9$

Step 6.1.1.2

Cancel the common factor of $17$ .

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Step 6.1.1.2.1

Factor $17$ out of $17 p$ .

$\frac{1}{17} (17 (p)) = \frac{15}{17} \cdot - 9$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{17} (17 p) = \frac{15}{17} \cdot - 9$

Step 6.1.1.2.3

Rewrite the expression.

$p = \frac{15}{17} \cdot - 9$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{15}{17} \cdot - 9$ .

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Step 6.2.1.1

Multiply $\frac{15}{17} \cdot - 9$ .

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Step 6.2.1.1.1

Combine $\frac{15}{17}$ and $- 9$ .

$p = \frac{15 \cdot - 9}{17}$

Step 6.2.1.1.2

Multiply $15$ by $- 9$ .

$p = \frac{- 135}{17}$

Step 6.2.1.2

Move the negative in front of the fraction.

$p = - \frac{135}{17}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{135}{17}$

Decimal Form:

$p = - 7.94117647 \dots$

Mixed Number Form:

$p = - 7 \frac{16}{17}$