Finite Math Examples

$\frac{x}{16} - \frac{5}{8} = \frac{x + 6}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{x}{16} - \frac{5}{8}) \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x}{16} - \frac{5}{8}) \cdot 8$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{x}{16} \cdot 8 - \frac{5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.2

Cancel the common factor of $8$ .

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Step 2.1.1.2.1

Factor $8$ out of $16$ .

$\frac{x}{8 (2)} \cdot 8 - \frac{5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{x}{8 \cdot 2} \cdot 8 - \frac{5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{x}{2} - \frac{5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.3

Cancel the common factor of $8$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$\frac{x}{2} + \frac{- 5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{x}{2} + \frac{- 5}{8} \cdot 8 = \frac{x + 6}{8} \cdot 8$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{x}{2} - 5 = \frac{x + 6}{8} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x}{2} - 5 = \frac{x + 6}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$\frac{x}{2} - 5 = x + 6$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{x}{2} - 5 - x = 6$

Step 3.1.2

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

$\frac{x}{2} - x \cdot \frac{2}{2} - 5 = 6$

Step 3.1.3

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

$\frac{x}{2} + \frac{- x \cdot 2}{2} - 5 = 6$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{2} - 5 = 6$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $x - x \cdot 2$ .

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Step 3.1.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{2} - 5 = 6$

Step 3.1.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{2} - 5 = 6$

Step 3.1.5.1.1.3

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{2} - 5 = 6$

Step 3.1.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 2)$ .

$\frac{x (1 - 1 \cdot 2)}{2} - 5 = 6$

Step 3.1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{2} - 5 = 6$

Step 3.1.5.1.3

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{2} - 5 = 6$

Step 3.1.5.2

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} - 5 = 6$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{x}{2} - 5 = 6$

Step 3.2

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

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Step 3.2.1

Add $5$ to both sides of the equation.

$- \frac{x}{2} = 6 + 5$

Step 3.2.2

Add $6$ and $5$ .

$- \frac{x}{2} = 11$

Step 3.3

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot 11$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $- 2 (- \frac{x}{2})$ .

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Step 3.4.1.1.1

Cancel the common factor of $2$ .

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Step 3.4.1.1.1.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 \cdot 11$

Step 3.4.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot 11$

Step 3.4.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 \cdot 11$

Step 3.4.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot 11$

Step 3.4.1.1.2

Multiply.

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Step 3.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 11$

Step 3.4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot 11$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $- 2$ by $11$ .

$x = - 22$