Finite Math Examples

$\frac{1}{3} \cdot (5 - 2) + 2 = \frac{1}{2} \cdot (x + 4)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (x + 4) = \frac{1}{3} \cdot (5 - 2) + 2$ .

$\frac{1}{2} \cdot (x + 4) = \frac{1}{3} \cdot (5 - 2) + 2$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x + 4)) = 2 (\frac{1}{3} \cdot (5 - 2) + 2)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (x + 4))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} \cdot 4) = 2 (\frac{1}{3} \cdot (5 - 2) + 2)$

Step 3.1.1.2

Combine $\frac{1}{2}$ and $x$ .

$2 (\frac{x}{2} + \frac{1}{2} \cdot 4) = 2 (\frac{1}{3} \cdot (5 - 2) + 2)$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Factor $2$ out of $4$ .

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

Step 3.1.1.3.2

Cancel the common factor.

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

Step 3.1.1.3.3

Rewrite the expression.

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

Step 3.1.1.4

Apply the distributive property.

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

Step 3.1.1.5

Cancel the common factor of $2$ .

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Step 3.1.1.5.1

Cancel the common factor.

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

Step 3.1.1.5.2

Rewrite the expression.

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

Step 3.1.1.6

Multiply $2$ by $2$ .

$x + 4 = 2 (\frac{1}{3} \cdot (5 - 2) + 2)$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Subtract $2$ from $5$ .

$x + 4 = 2 (\frac{1}{3} \cdot 3 + 2)$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$x + 4 = 2 (\frac{1}{3} \cdot 3 + 2)$

Step 3.2.1.1.2.2

Rewrite the expression.

$x + 4 = 2 (1 + 2)$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Add $1$ and $2$ .

$x + 4 = 2 \cdot 3$

Step 3.2.1.2.2

Multiply $2$ by $3$ .

$x + 4 = 6$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$x = 6 - 4$

Step 4.2

Subtract $4$ from $6$ .

$x = 2$