Finite Math Examples

$\frac{1}{8} x - \frac{1}{11} x + \frac{1}{88} x = 8$

Step 1

Simplify $\frac{1}{8} x - \frac{1}{11} x + \frac{1}{88} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{8}$ and $x$ .

$\frac{x}{8} - \frac{1}{11} x + \frac{1}{88} x = 8$

Step 1.1.2

Combine $x$ and $\frac{1}{11}$ .

$\frac{x}{8} - \frac{x}{11} + \frac{1}{88} x = 8$

Step 1.1.3

Combine $\frac{1}{88}$ and $x$ .

$\frac{x}{8} - \frac{x}{11} + \frac{x}{88} = 8$

Step 1.2

Find the common denominator.

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Step 1.2.1

Multiply $\frac{x}{8}$ by $\frac{11}{11}$ .

$\frac{x}{8} \cdot \frac{11}{11} - \frac{x}{11} + \frac{x}{88} = 8$

Step 1.2.2

Multiply $\frac{x}{8}$ by $\frac{11}{11}$ .

$\frac{x \cdot 11}{8 \cdot 11} - \frac{x}{11} + \frac{x}{88} = 8$

Step 1.2.3

Multiply $\frac{x}{11}$ by $\frac{8}{8}$ .

$\frac{x \cdot 11}{8 \cdot 11} - (\frac{x}{11} \cdot \frac{8}{8}) + \frac{x}{88} = 8$

Step 1.2.4

Multiply $\frac{x}{11}$ by $\frac{8}{8}$ .

$\frac{x \cdot 11}{8 \cdot 11} - \frac{x \cdot 8}{11 \cdot 8} + \frac{x}{88} = 8$

Step 1.2.5

Multiply $8$ by $11$ .

$\frac{x \cdot 11}{88} - \frac{x \cdot 8}{11 \cdot 8} + \frac{x}{88} = 8$

Step 1.2.6

Reorder the factors of $11 \cdot 8$ .

$\frac{x \cdot 11}{88} - \frac{x \cdot 8}{8 \cdot 11} + \frac{x}{88} = 8$

Step 1.2.7

Multiply $8$ by $11$ .

$\frac{x \cdot 11}{88} - \frac{x \cdot 8}{88} + \frac{x}{88} = 8$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 11 - x \cdot 8 + x}{88} = 8$

Step 1.4

Simplify each term.

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Step 1.4.1

Move $11$ to the left of $x$ .

$\frac{11 \cdot x - x \cdot 8 + x}{88} = 8$

Step 1.4.2

Multiply $8$ by $- 1$ .

$\frac{11 x - 8 x + x}{88} = 8$

Step 1.5

Simplify terms.

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Step 1.5.1

Subtract $8 x$ from $11 x$ .

$\frac{3 x + x}{88} = 8$

Step 1.5.2

Add $3 x$ and $x$ .

$\frac{4 x}{88} = 8$

Step 1.5.3

Cancel the common factor of $4$ and $88$ .

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Step 1.5.3.1

Factor $4$ out of $4 x$ .

$\frac{4 (x)}{88} = 8$

Step 1.5.3.2

Cancel the common factors.

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Step 1.5.3.2.1

Factor $4$ out of $88$ .

$\frac{4 x}{4 \cdot 22} = 8$

Step 1.5.3.2.2

Cancel the common factor.

$\frac{4 x}{4 \cdot 22} = 8$

Step 1.5.3.2.3

Rewrite the expression.

$\frac{x}{22} = 8$

Step 2

Multiply both sides of the equation by $22$ .

$22 \frac{x}{22} = 22 \cdot 8$

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

Cancel the common factor of $22$ .

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Step 3.1.1.1

Cancel the common factor.

$22 \frac{x}{22} = 22 \cdot 8$

Step 3.1.1.2

Rewrite the expression.

$x = 22 \cdot 8$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $22$ by $8$ .

$x = 176$