Finite Math Examples

$\frac{1}{6} x - \frac{1}{7} x + \frac{1}{42} x = 6$

Step 1

Simplify $\frac{1}{6} x - \frac{1}{7} x + \frac{1}{42} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{6} - \frac{1}{7} x + \frac{1}{42} x = 6$

Step 1.1.2

Combine $x$ and $\frac{1}{7}$ .

$\frac{x}{6} - \frac{x}{7} + \frac{1}{42} x = 6$

Step 1.1.3

Combine $\frac{1}{42}$ and $x$ .

$\frac{x}{6} - \frac{x}{7} + \frac{x}{42} = 6$

Step 1.2

Find the common denominator.

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Step 1.2.1

Multiply $\frac{x}{6}$ by $\frac{7}{7}$ .

$\frac{x}{6} \cdot \frac{7}{7} - \frac{x}{7} + \frac{x}{42} = 6$

Step 1.2.2

Multiply $\frac{x}{6}$ by $\frac{7}{7}$ .

$\frac{x \cdot 7}{6 \cdot 7} - \frac{x}{7} + \frac{x}{42} = 6$

Step 1.2.3

Multiply $\frac{x}{7}$ by $\frac{6}{6}$ .

$\frac{x \cdot 7}{6 \cdot 7} - (\frac{x}{7} \cdot \frac{6}{6}) + \frac{x}{42} = 6$

Step 1.2.4

Multiply $\frac{x}{7}$ by $\frac{6}{6}$ .

$\frac{x \cdot 7}{6 \cdot 7} - \frac{x \cdot 6}{7 \cdot 6} + \frac{x}{42} = 6$

Step 1.2.5

Multiply $6$ by $7$ .

$\frac{x \cdot 7}{42} - \frac{x \cdot 6}{7 \cdot 6} + \frac{x}{42} = 6$

Step 1.2.6

Reorder the factors of $7 \cdot 6$ .

$\frac{x \cdot 7}{42} - \frac{x \cdot 6}{6 \cdot 7} + \frac{x}{42} = 6$

Step 1.2.7

Multiply $6$ by $7$ .

$\frac{x \cdot 7}{42} - \frac{x \cdot 6}{42} + \frac{x}{42} = 6$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 7 - x \cdot 6 + x}{42} = 6$

Step 1.4

Simplify each term.

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Step 1.4.1

Move $7$ to the left of $x$ .

$\frac{7 \cdot x - x \cdot 6 + x}{42} = 6$

Step 1.4.2

Multiply $6$ by $- 1$ .

$\frac{7 x - 6 x + x}{42} = 6$

Step 1.5

Simplify terms.

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Step 1.5.1

Subtract $6 x$ from $7 x$ .

$\frac{x + x}{42} = 6$

Step 1.5.2

Add $x$ and $x$ .

$\frac{2 x}{42} = 6$

Step 1.5.3

Cancel the common factor of $2$ and $42$ .

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Step 1.5.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{42} = 6$

Step 1.5.3.2

Cancel the common factors.

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Step 1.5.3.2.1

Factor $2$ out of $42$ .

$\frac{2 x}{2 \cdot 21} = 6$

Step 1.5.3.2.2

Cancel the common factor.

$\frac{2 x}{2 \cdot 21} = 6$

Step 1.5.3.2.3

Rewrite the expression.

$\frac{x}{21} = 6$

Step 2

Multiply both sides of the equation by $21$ .

$21 \frac{x}{21} = 21 \cdot 6$

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 $21$ .

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Step 3.1.1.1

Cancel the common factor.

$21 \frac{x}{21} = 21 \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$x = 21 \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $21$ by $6$ .

$x = 126$