Solve for p 6(p+2.25)=15 9/10

$6 (p + 2.25) = 15 \frac{9}{10}$

Step 1

Simplify the left side.

Simplify $6 (p + 2.25)$ .

Apply the distributive property.

$6 p + 6 \cdot 2.25 = 15 \frac{9}{10}$

Multiply $6$ by $2.25$ .

$6 p + 13.5 = 15 \frac{9}{10}$

Step 2

Simplify the right side.

Convert $15 \frac{9}{10}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$6 p + 13.5 = 15 + \frac{9}{10}$

Add $15$ and $\frac{9}{10}$ .

To write $15$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$6 p + 13.5 = 15 \cdot \frac{10}{10} + \frac{9}{10}$

Combine $15$ and $\frac{10}{10}$ .

$6 p + 13.5 = \frac{15 \cdot 10}{10} + \frac{9}{10}$

Combine the numerators over the common denominator.

$6 p + 13.5 = \frac{15 \cdot 10 + 9}{10}$

Simplify the numerator.

Multiply $15$ by $10$ .

$6 p + 13.5 = \frac{150 + 9}{10}$

Add $150$ and $9$ .

$6 p + 13.5 = \frac{159}{10}$

Step 3

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

Subtract $13.5$ from both sides of the equation.

$6 p = \frac{159}{10} - 13.5$

To write $- 13.5$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$6 p = \frac{159}{10} - 13.5 \cdot \frac{10}{10}$

Combine $- 13.5$ and $\frac{10}{10}$ .

$6 p = \frac{159}{10} + \frac{- 13.5 \cdot 10}{10}$

Combine the numerators over the common denominator.

$6 p = \frac{159 - 13.5 \cdot 10}{10}$

Simplify the numerator.

Multiply $- 13.5$ by $10$ .

$6 p = \frac{159 - 135}{10}$

Subtract $135$ from $159$ .

$6 p = \frac{24}{10}$

Cancel the common factor of $24$ and $10$ .

Factor $2$ out of $24$ .

$6 p = \frac{2 (12)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$6 p = \frac{2 \cdot 12}{2 \cdot 5}$

Cancel the common factor.

$6 p = \frac{2 \cdot 12}{2 \cdot 5}$

Rewrite the expression.

$6 p = \frac{12}{5}$

Step 4

Divide each term in $6 p = \frac{12}{5}$ by $6$ and simplify.

Divide each term in $6 p = \frac{12}{5}$ by $6$ .

$\frac{6 p}{6} = \frac{\frac{12}{5}}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 p}{6} = \frac{\frac{12}{5}}{6}$

Divide $p$ by $1$ .

$p = \frac{\frac{12}{5}}{6}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$p = \frac{12}{5} \cdot \frac{1}{6}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$p = \frac{6 (2)}{5} \cdot \frac{1}{6}$

Cancel the common factor.

$p = \frac{6 \cdot 2}{5} \cdot \frac{1}{6}$

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$p = 0.4$

Solve for p 6(p+2.25)=15 9/10

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