Algebra Examples

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

Step 1

Combine $\frac{3}{5}$ and $p$ .

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

Step 2

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

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Step 2.1

Subtract $\frac{3 p}{5}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Move $5$ to the left of $p$ .

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

Step 2.7

Subtract $3 p$ from $5 p$ .

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

Step 2.8

Factor $2$ out of $2 + 2 p$ .

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Step 2.8.1

Factor $2$ out of $2$ .

$\frac{2 \cdot 1 + 2 p}{5} = \frac{4}{5}$

Step 2.8.2

Factor $2$ out of $2 \cdot 1 + 2 p$ .

$\frac{2 (1 + p)}{5} = \frac{4}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 (1 + p) = 4$

Step 4

Divide each term in $2 (1 + p) = 4$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 (1 + p) = 4$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $1 + p$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $4$ by $2$ .

$1 + p = 2$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$p = 2 - 1$

Step 5.2

Subtract $1$ from $2$ .

$p = 1$