Algebra Examples

$- 8 p = 20 (\frac{4}{5} p + 3 - \frac{3}{4} p)$

Step 1

Since $p$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$20 (\frac{4}{5} p + 3 - \frac{3}{4} p) = - 8 p$

Step 2

Simplify $20 (\frac{4}{5} p + 3 - \frac{3}{4} p)$ .

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Step 2.1

Rewrite.

$0 + 0 + 20 (\frac{4}{5} p + 3 - \frac{3}{4} p) = - 8 p$

Step 2.2

Simplify by adding zeros.

$20 (\frac{4}{5} p + 3 - \frac{3}{4} p) = - 8 p$

Step 2.3

Simplify each term.

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Step 2.3.1

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

$20 (\frac{4 p}{5} + 3 - \frac{3}{4} p) = - 8 p$

Step 2.3.2

Combine $p$ and $\frac{3}{4}$ .

$20 (\frac{4 p}{5} + 3 - \frac{p \cdot 3}{4}) = - 8 p$

Step 2.3.3

Move $3$ to the left of $p$ .

$20 (\frac{4 p}{5} + 3 - \frac{3 p}{4}) = - 8 p$

Step 2.4

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

$20 (\frac{4 p}{5} \cdot \frac{4}{4} - \frac{3 p}{4} + 3) = - 8 p$

Step 2.5

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

$20 (\frac{4 p}{5} \cdot \frac{4}{4} - \frac{3 p}{4} \cdot \frac{5}{5} + 3) = - 8 p$

Step 2.6

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

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

$20 (\frac{4 p \cdot 4}{5 \cdot 4} - \frac{3 p}{4} \cdot \frac{5}{5} + 3) = - 8 p$

Step 2.6.2

Multiply $5$ by $4$ .

$20 (\frac{4 p \cdot 4}{20} - \frac{3 p}{4} \cdot \frac{5}{5} + 3) = - 8 p$

Step 2.6.3

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

$20 (\frac{4 p \cdot 4}{20} - \frac{3 p \cdot 5}{4 \cdot 5} + 3) = - 8 p$

Step 2.6.4

Multiply $4$ by $5$ .

$20 (\frac{4 p \cdot 4}{20} - \frac{3 p \cdot 5}{20} + 3) = - 8 p$

Step 2.7

Combine the numerators over the common denominator.

$20 (\frac{4 p \cdot 4 - 3 p \cdot 5}{20} + 3) = - 8 p$

Step 2.8

Simplify each term.

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Step 2.8.1

Simplify the numerator.

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Step 2.8.1.1

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

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Step 2.8.1.1.1

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

$20 (\frac{p (4 \cdot 4) - 3 p \cdot 5}{20} + 3) = - 8 p$

Step 2.8.1.1.2

Factor $p$ out of $- 3 p \cdot 5$ .

$20 (\frac{p (4 \cdot 4) + p (- 3 \cdot 5)}{20} + 3) = - 8 p$

Step 2.8.1.1.3

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

$20 (\frac{p (4 \cdot 4 - 3 \cdot 5)}{20} + 3) = - 8 p$

Step 2.8.1.2

Multiply $4$ by $4$ .

$20 (\frac{p (16 - 3 \cdot 5)}{20} + 3) = - 8 p$

Step 2.8.1.3

Multiply $- 3$ by $5$ .

$20 (\frac{p (16 - 15)}{20} + 3) = - 8 p$

Step 2.8.1.4

Subtract $15$ from $16$ .

$20 (\frac{p \cdot 1}{20} + 3) = - 8 p$

Step 2.8.2

Multiply $p$ by $1$ .

$20 (\frac{p}{20} + 3) = - 8 p$

Step 2.9

Simplify terms.

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Step 2.9.1

Apply the distributive property.

$20 \frac{p}{20} + 20 \cdot 3 = - 8 p$

Step 2.9.2

Cancel the common factor of $20$ .

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Step 2.9.2.1

Cancel the common factor.

$20 \frac{p}{20} + 20 \cdot 3 = - 8 p$

Step 2.9.2.2

Rewrite the expression.

$p + 20 \cdot 3 = - 8 p$

Step 2.9.3

Multiply $20$ by $3$ .

$p + 60 = - 8 p$

Step 3

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

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Step 3.1

Add $8 p$ to both sides of the equation.

$p + 60 + 8 p = 0$

Step 3.2

Add $p$ and $8 p$ .

$9 p + 60 = 0$

Step 4

Subtract $60$ from both sides of the equation.

$9 p = - 60$

Step 5

Divide each term in $9 p = - 60$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 p = - 60$ by $9$ .

$\frac{9 p}{9} = \frac{- 60}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 p}{9} = \frac{- 60}{9}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 60}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 60$ and $9$ .

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Step 5.3.1.1

Factor $3$ out of $- 60$ .

$p = \frac{3 (- 20)}{9}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $3$ out of $9$ .

$p = \frac{3 \cdot - 20}{3 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$p = \frac{3 \cdot - 20}{3 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

$p = \frac{- 20}{3}$

Step 5.3.2

Move the negative in front of the fraction.

$p = - \frac{20}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{20}{3}$

Decimal Form:

$p = - 6.\overline{6}$

Mixed Number Form:

$p = - 6 \frac{2}{3}$