Algebra Examples

$\frac{3}{2} p - 5 + \frac{9}{4} p = 7 - \frac{5}{4} p$

Step 1

Simplify $\frac{3}{2} p - 5 + \frac{9}{4} p$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{3 p}{2} - 5 + \frac{9}{4} p = 7 - \frac{5}{4} p$

Step 1.1.2

Combine $\frac{9}{4}$ and $p$ .

$\frac{3 p}{2} - 5 + \frac{9 p}{4} = 7 - \frac{5}{4} p$

Step 1.2

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

$\frac{3 p}{2} \cdot \frac{2}{2} + \frac{9 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 p}{2}$ by $\frac{2}{2}$ .

$\frac{3 p \cdot 2}{2 \cdot 2} + \frac{9 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3 p \cdot 2}{4} + \frac{9 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 p \cdot 2 + 9 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $3 p$ out of $3 p \cdot 2 + 9 p$ .

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Step 1.5.1.1

Factor $3 p$ out of $3 p \cdot 2$ .

$\frac{3 p (2) + 9 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.5.1.2

Factor $3 p$ out of $9 p$ .

$\frac{3 p (2) + 3 p (3)}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.5.1.3

Factor $3 p$ out of $3 p (2) + 3 p (3)$ .

$\frac{3 p (2 + 3)}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.5.2

Add $2$ and $3$ .

$\frac{3 p \cdot 5}{4} - 5 = 7 - \frac{5}{4} p$

Step 1.5.3

Multiply $5$ by $3$ .

$\frac{15 p}{4} - 5 = 7 - \frac{5}{4} p$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{15 p}{4} - 5 = 7 - \frac{p \cdot 5}{4}$

Step 2.2

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

$\frac{15 p}{4} - 5 = 7 - \frac{5 p}{4}$

Step 3

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

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Step 3.1

Add $\frac{5 p}{4}$ to both sides of the equation.

$\frac{15 p}{4} - 5 + \frac{5 p}{4} = 7$

Step 3.2

Combine the numerators over the common denominator.

$- 5 + \frac{15 p + 5 p}{4} = 7$

Step 3.3

Add $15 p$ and $5 p$ .

$- 5 + \frac{20 p}{4} = 7$

Step 3.4

Cancel the common factor of $20$ and $4$ .

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Step 3.4.1

Factor $4$ out of $20 p$ .

$- 5 + \frac{4 (5 p)}{4} = 7$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $4$ out of $4$ .

$- 5 + \frac{4 (5 p)}{4 (1)} = 7$

Step 3.4.2.2

Cancel the common factor.

$- 5 + \frac{4 (5 p)}{4 \cdot 1} = 7$

Step 3.4.2.3

Rewrite the expression.

$- 5 + \frac{5 p}{1} = 7$

Step 3.4.2.4

Divide $5 p$ by $1$ .

$- 5 + 5 p = 7$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$5 p = 7 + 5$

Step 4.2

Add $7$ and $5$ .

$5 p = 12$

Step 5

Divide each term in $5 p = 12$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 p = 12$ by $5$ .

$\frac{5 p}{5} = \frac{12}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 p}{5} = \frac{12}{5}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{12}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{12}{5}$

Decimal Form:

$p = 2.4$

Mixed Number Form:

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