Pre-Algebra Examples

$\frac{1}{9} \cdot (a + 4) = \frac{1}{3} \cdot (3 - a)$

Step 1

Simplify $\frac{1}{9} \cdot (a + 4)$ .

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Step 1.1

Apply the distributive property.

$\frac{1}{9} a + \frac{1}{9} \cdot 4 = \frac{1}{3} \cdot (3 - a)$

Step 1.2

Combine $\frac{1}{9}$ and $a$ .

$\frac{a}{9} + \frac{1}{9} \cdot 4 = \frac{1}{3} \cdot (3 - a)$

Step 1.3

Combine $\frac{1}{9}$ and $4$ .

$\frac{a}{9} + \frac{4}{9} = \frac{1}{3} \cdot (3 - a)$

Step 2

Simplify $\frac{1}{3} \cdot (3 - a)$ .

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Step 2.1

Apply the distributive property.

$\frac{a}{9} + \frac{4}{9} = \frac{1}{3} \cdot 3 + \frac{1}{3} (- a)$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Cancel the common factor.

$\frac{a}{9} + \frac{4}{9} = \frac{1}{3} \cdot 3 + \frac{1}{3} (- a)$

Step 2.2.2

Rewrite the expression.

$\frac{a}{9} + \frac{4}{9} = 1 + \frac{1}{3} (- a)$

Step 2.3

Combine $\frac{1}{3}$ and $a$ .

$\frac{a}{9} + \frac{4}{9} = 1 - \frac{a}{3}$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$a = \frac{5}{4}$

Step 4