Finite Math Examples

$2 + \frac{x}{2} + \frac{3 x}{8} = 16$

Step 1

Simplify $2 + \frac{x}{2} + \frac{3 x}{8}$ .

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Step 1.1

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 + \frac{x}{2} \cdot \frac{4}{4} + \frac{3 x}{8} = 16$

Step 1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{x}{2}$ by $\frac{4}{4}$ .

$2 + \frac{x \cdot 4}{2 \cdot 4} + \frac{3 x}{8} = 16$

Step 1.2.2

Multiply $2$ by $4$ .

$2 + \frac{x \cdot 4}{8} + \frac{3 x}{8} = 16$

Step 1.3

Combine the numerators over the common denominator.

$2 + \frac{x \cdot 4 + 3 x}{8} = 16$

Step 1.4

Add $x \cdot 4$ and $3 x$ .

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Step 1.4.1

Reorder $x$ and $4$ .

$2 + \frac{4 \cdot x + 3 x}{8} = 16$

Step 1.4.2

Add $4 \cdot x$ and $3 x$ .

$2 + \frac{7 \cdot x}{8} = 16$

$2 + \frac{7 x}{8} = 16$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$\frac{7 x}{8} = 16 - 2$

Step 2.2

Subtract $2$ from $16$ .

$\frac{7 x}{8} = 14$

Step 3

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot 14$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{8}{7} \cdot \frac{7 x}{8}$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot 14$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot 14$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{8}{7} \cdot 14$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot 14$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{8}{7} \cdot 14$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{8}{7} \cdot 14$ .

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Step 4.2.1.1

Cancel the common factor of $7$ .

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Step 4.2.1.1.1

Factor $7$ out of $14$ .

$x = \frac{8}{7} \cdot (7 (2))$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{8}{7} \cdot (7 \cdot 2)$

Step 4.2.1.1.3

Rewrite the expression.

$x = 8 \cdot 2$

Step 4.2.1.2

Multiply $8$ by $2$ .

$x = 16$