Finite Math Examples

$- \frac{1}{6} x - \frac{5}{2} - \frac{3 - 6 x}{5} = 0$

Step 1

Simplify $- \frac{1}{6} x - \frac{5}{2} - \frac{3 - 6 x}{5}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$- \frac{x}{6} - \frac{5}{2} - \frac{3 - 6 x}{5} = 0$

Step 1.1.2

Factor $3$ out of $3 - 6 x$ .

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Step 1.1.2.1

Factor $3$ out of $3$ .

$- \frac{x}{6} - \frac{5}{2} - \frac{3 (1) - 6 x}{5} = 0$

Step 1.1.2.2

Factor $3$ out of $- 6 x$ .

$- \frac{x}{6} - \frac{5}{2} - \frac{3 (1) + 3 (- 2 x)}{5} = 0$

Step 1.1.2.3

Factor $3$ out of $3 (1) + 3 (- 2 x)$ .

$- \frac{x}{6} - \frac{5}{2} - \frac{3 (1 - 2 x)}{5} = 0$

Step 1.2

To write $- \frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x}{6} \cdot \frac{5}{5} - \frac{3 (1 - 2 x)}{5} - \frac{5}{2} = 0$

Step 1.3

To write $- \frac{3 (1 - 2 x)}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{x}{6} \cdot \frac{5}{5} - \frac{3 (1 - 2 x)}{5} \cdot \frac{6}{6} - \frac{5}{2} = 0$

Step 1.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{x}{6}$ by $\frac{5}{5}$ .

$- \frac{x \cdot 5}{6 \cdot 5} - \frac{3 (1 - 2 x)}{5} \cdot \frac{6}{6} - \frac{5}{2} = 0$

Step 1.4.2

Multiply $6$ by $5$ .

$- \frac{x \cdot 5}{30} - \frac{3 (1 - 2 x)}{5} \cdot \frac{6}{6} - \frac{5}{2} = 0$

Step 1.4.3

Multiply $\frac{3 (1 - 2 x)}{5}$ by $\frac{6}{6}$ .

$- \frac{x \cdot 5}{30} - \frac{3 (1 - 2 x) \cdot 6}{5 \cdot 6} - \frac{5}{2} = 0$

Step 1.4.4

Multiply $5$ by $6$ .

$- \frac{x \cdot 5}{30} - \frac{3 (1 - 2 x) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.5

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 - 3 (1 - 2 x) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $5$ by $- 1$ .

$\frac{- 5 x - 3 (1 - 2 x) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.2

Apply the distributive property.

$\frac{- 5 x + (- 3 \cdot 1 - 3 (- 2 x)) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.3

Multiply $- 3$ by $1$ .

$\frac{- 5 x + (- 3 - 3 (- 2 x)) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.4

Multiply $- 2$ by $- 3$ .

$\frac{- 5 x + (- 3 + 6 x) \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.5

Apply the distributive property.

$\frac{- 5 x - 3 \cdot 6 + 6 x \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.6

Multiply $- 3$ by $6$ .

$\frac{- 5 x - 18 + 6 x \cdot 6}{30} - \frac{5}{2} = 0$

Step 1.6.7

Multiply $6$ by $6$ .

$\frac{- 5 x - 18 + 36 x}{30} - \frac{5}{2} = 0$

Step 1.6.8

Add $- 5 x$ and $36 x$ .

$\frac{31 x - 18}{30} - \frac{5}{2} = 0$

Step 1.7

To write $- \frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{31 x - 18}{30} - \frac{5}{2} \cdot \frac{15}{15} = 0$

Step 1.8

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{5}{2}$ by $\frac{15}{15}$ .

$\frac{31 x - 18}{30} - \frac{5 \cdot 15}{2 \cdot 15} = 0$

Step 1.8.2

Multiply $2$ by $15$ .

$\frac{31 x - 18}{30} - \frac{5 \cdot 15}{30} = 0$

Step 1.9

Combine the numerators over the common denominator.

$\frac{31 x - 18 - 5 \cdot 15}{30} = 0$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Multiply $- 5$ by $15$ .

$\frac{31 x - 18 - 75}{30} = 0$

Step 1.10.2

Subtract $75$ from $- 18$ .

$\frac{31 x - 93}{30} = 0$

Step 1.10.3

Factor $31$ out of $31 x - 93$ .

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Step 1.10.3.1

Factor $31$ out of $31 x$ .

$\frac{31 (x) - 93}{30} = 0$

Step 1.10.3.2

Factor $31$ out of $- 93$ .

$\frac{31 x + 31 \cdot - 3}{30} = 0$

Step 1.10.3.3

Factor $31$ out of $31 x + 31 \cdot - 3$ .

$\frac{31 (x - 3)}{30} = 0$

Step 2

Set the numerator equal to zero.

$31 (x - 3) = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Divide each term in $31 (x - 3) = 0$ by $31$ and simplify.

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Step 3.1.1

Divide each term in $31 (x - 3) = 0$ by $31$ .

$\frac{31 (x - 3)}{31} = \frac{0}{31}$

Step 3.1.2

Simplify the left side.

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Step 3.1.2.1

Cancel the common factor of $31$ .

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Step 3.1.2.1.1

Cancel the common factor.

$\frac{31 (x - 3)}{31} = \frac{0}{31}$

Step 3.1.2.1.2

Divide $x - 3$ by $1$ .

$x - 3 = \frac{0}{31}$

Step 3.1.3

Simplify the right side.

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Step 3.1.3.1

Divide $0$ by $31$ .

$x - 3 = 0$

Step 3.2

Add $3$ to both sides of the equation.

$x = 3$