Finite Math Examples

$\frac{1}{6} \cdot (9 x - 5) = \frac{x + 5}{12}$

Step 1

Multiply both sides by $12$ .

$\frac{1}{6} \cdot (9 x - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1}{6} \cdot (9 x - 5) \cdot 12$ .

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Step 2.1.1.1

Apply the distributive property.

$(\frac{1}{6} (9 x) + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $6$ .

$(\frac{1}{3 (2)} (9 x) + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.2.2

Factor $3$ out of $9 x$ .

$(\frac{1}{3 (2)} (3 (3 x)) + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.2.3

Cancel the common factor.

$(\frac{1}{3 \cdot 2} (3 (3 x)) + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.2.4

Rewrite the expression.

$(\frac{1}{2} (3 x) + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.3

Combine $3$ and $\frac{1}{2}$ .

$(\frac{3}{2} x + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.4

Combine $\frac{3}{2}$ and $x$ .

$(\frac{3 x}{2} + \frac{1}{6} \cdot - 5) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.5

Combine $\frac{1}{6}$ and $- 5$ .

$(\frac{3 x}{2} + \frac{- 5}{6}) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.6

Move the negative in front of the fraction.

$(\frac{3 x}{2} - \frac{5}{6}) \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.7

Apply the distributive property.

$\frac{3 x}{2} \cdot 12 - \frac{5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $12$ .

$\frac{3 x}{2} \cdot (2 (6)) - \frac{5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{3 x}{2} \cdot (2 \cdot 6) - \frac{5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.8.3

Rewrite the expression.

$3 x \cdot 6 - \frac{5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.9

Multiply $6$ by $3$ .

$18 x - \frac{5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.10

Cancel the common factor of $6$ .

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Step 2.1.1.10.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$18 x + \frac{- 5}{6} \cdot 12 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.10.2

Factor $6$ out of $12$ .

$18 x + \frac{- 5}{6} \cdot (6 (2)) = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.10.3

Cancel the common factor.

$18 x + \frac{- 5}{6} \cdot (6 \cdot 2) = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.10.4

Rewrite the expression.

$18 x - 5 \cdot 2 = \frac{x + 5}{12} \cdot 12$

Step 2.1.1.11

Multiply $- 5$ by $2$ .

$18 x - 10 = \frac{x + 5}{12} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$18 x - 10 = \frac{x + 5}{12} \cdot 12$

Step 2.2.1.2

Rewrite the expression.

$18 x - 10 = x + 5$

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.

$18 x - 10 - x = 5$

Step 3.1.2

Subtract $x$ from $18 x$ .

$17 x - 10 = 5$

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 $10$ to both sides of the equation.

$17 x = 5 + 10$

Step 3.2.2

Add $5$ and $10$ .

$17 x = 15$

Step 3.3

Divide each term in $17 x = 15$ by $17$ and simplify.

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Step 3.3.1

Divide each term in $17 x = 15$ by $17$ .

$\frac{17 x}{17} = \frac{15}{17}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $17$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{17 x}{17} = \frac{15}{17}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{17}$

Decimal Form:

$x = 0.88235294 \dots$