Algebra Examples

$\frac{2}{3} - 2 p = 5 + \frac{4}{3} p$

Step 1

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

$\frac{2}{3} - 2 p = 5 + \frac{4 p}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{4 p}{3}$ from both sides of the equation.

$\frac{2}{3} - 2 p - \frac{4 p}{3} = 5$

Step 2.2

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

$\frac{2}{3} - 2 p \cdot \frac{3}{3} - \frac{4 p}{3} = 5$

Step 2.3

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

$\frac{2}{3} + \frac{- 2 p \cdot 3}{3} - \frac{4 p}{3} = 5$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2}{3} + \frac{- 2 p \cdot 3 - 4 p}{3} = 5$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2 - 2 p \cdot 3 - 4 p}{3} = 5$

Step 2.6

Multiply $3$ by $- 2$ .

$\frac{2 - 6 p - 4 p}{3} = 5$

Step 2.7

Subtract $4 p$ from $- 6 p$ .

$\frac{2 - 10 p}{3} = 5$

Step 2.8

Factor $2$ out of $2 - 10 p$ .

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Step 2.8.1

Factor $2$ out of $2$ .

$\frac{2 (1) - 10 p}{3} = 5$

Step 2.8.2

Factor $2$ out of $- 10 p$ .

$\frac{2 (1) + 2 (- 5 p)}{3} = 5$

Step 2.8.3

Factor $2$ out of $2 (1) + 2 (- 5 p)$ .

$\frac{2 (1 - 5 p)}{3} = 5$

Step 3

Multiply both sides by $3$ .

$\frac{2 (1 - 5 p)}{3} \cdot 3 = 5 \cdot 3$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2 (1 - 5 p)}{3} \cdot 3$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2 (1 - 5 p)}{3} \cdot 3 = 5 \cdot 3$

Step 4.1.1.1.2

Rewrite the expression.

$2 (1 - 5 p) = 5 \cdot 3$

Step 4.1.1.2

Apply the distributive property.

$2 \cdot 1 + 2 (- 5 p) = 5 \cdot 3$

Step 4.1.1.3

Simplify the expression.

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Step 4.1.1.3.1

Multiply $2$ by $1$ .

$2 + 2 (- 5 p) = 5 \cdot 3$

Step 4.1.1.3.2

Multiply $- 5$ by $2$ .

$2 - 10 p = 5 \cdot 3$

Step 4.1.1.3.3

Reorder $2$ and $- 10 p$ .

$- 10 p + 2 = 5 \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $5$ by $3$ .

$- 10 p + 2 = 15$

Step 5

Solve for $p$ .

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Step 5.1

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

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Step 5.1.1

Subtract $2$ from both sides of the equation.

$- 10 p = 15 - 2$

Step 5.1.2

Subtract $2$ from $15$ .

$- 10 p = 13$

Step 5.2

Divide each term in $- 10 p = 13$ by $- 10$ and simplify.

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Step 5.2.1

Divide each term in $- 10 p = 13$ by $- 10$ .

$\frac{- 10 p}{- 10} = \frac{13}{- 10}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 10$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 10 p}{- 10} = \frac{13}{- 10}$

Step 5.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{13}{- 10}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Move the negative in front of the fraction.

$p = - \frac{13}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{13}{10}$

Decimal Form:

$p = - 1.3$

Mixed Number Form:

$p = - 1 \frac{3}{10}$