Finite Math Examples

$\frac{- 7 x}{16} + \frac{4}{16} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1

Simplify $\frac{- 7 x}{16} + \frac{4}{16} + \frac{7}{- 3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Move the negative in front of the fraction.

$- \frac{7 x}{16} + \frac{4}{16} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1.1.2

Cancel the common factor of $4$ and $16$ .

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Step 1.1.2.1

Factor $4$ out of $4$ .

$- \frac{7 x}{16} + \frac{4 (1)}{16} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1.1.2.2

Cancel the common factors.

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Step 1.1.2.2.1

Factor $4$ out of $16$ .

$- \frac{7 x}{16} + \frac{4 \cdot 1}{4 \cdot 4} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1.1.2.2.2

Cancel the common factor.

$- \frac{7 x}{16} + \frac{4 \cdot 1}{4 \cdot 4} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1.1.2.2.3

Rewrite the expression.

$- \frac{7 x}{16} + \frac{1}{4} + \frac{7}{- 3} = - 4 - \frac{2 x + 2}{17}$

Step 1.1.3

Move the negative in front of the fraction.

$- \frac{7 x}{16} + \frac{1}{4} - \frac{7}{3} = - 4 - \frac{2 x + 2}{17}$

Step 1.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7 x}{16} + \frac{1}{4} \cdot \frac{3}{3} - \frac{7}{3} = - 4 - \frac{2 x + 2}{17}$

Step 1.3

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7 x}{16} + \frac{1}{4} \cdot \frac{3}{3} - \frac{7}{3} \cdot \frac{4}{4} = - 4 - \frac{2 x + 2}{17}$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$- \frac{7 x}{16} + \frac{3}{4 \cdot 3} - \frac{7}{3} \cdot \frac{4}{4} = - 4 - \frac{2 x + 2}{17}$

Step 1.4.2

Multiply $4$ by $3$ .

$- \frac{7 x}{16} + \frac{3}{12} - \frac{7}{3} \cdot \frac{4}{4} = - 4 - \frac{2 x + 2}{17}$

Step 1.4.3

Multiply $\frac{7}{3}$ by $\frac{4}{4}$ .

$- \frac{7 x}{16} + \frac{3}{12} - \frac{7 \cdot 4}{3 \cdot 4} = - 4 - \frac{2 x + 2}{17}$

Step 1.4.4

Multiply $3$ by $4$ .

$- \frac{7 x}{16} + \frac{3}{12} - \frac{7 \cdot 4}{12} = - 4 - \frac{2 x + 2}{17}$

Step 1.5

Combine the numerators over the common denominator.

$- \frac{7 x}{16} + \frac{3 - 7 \cdot 4}{12} = - 4 - \frac{2 x + 2}{17}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 7$ by $4$ .

$- \frac{7 x}{16} + \frac{3 - 28}{12} = - 4 - \frac{2 x + 2}{17}$

Step 1.6.2

Subtract $28$ from $3$ .

$- \frac{7 x}{16} + \frac{- 25}{12} = - 4 - \frac{2 x + 2}{17}$

Step 1.7

Move the negative in front of the fraction.

$- \frac{7 x}{16} - \frac{25}{12} = - 4 - \frac{2 x + 2}{17}$

Step 2

Simplify $- 4 - \frac{2 x + 2}{17}$ .

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Step 2.1

Factor $2$ out of $2 x + 2$ .

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Step 2.1.1

Factor $2$ out of $2 x$ .

$- \frac{7 x}{16} - \frac{25}{12} = - 4 - \frac{2 (x) + 2}{17}$

Step 2.1.2

Factor $2$ out of $2$ .

$- \frac{7 x}{16} - \frac{25}{12} = - 4 - \frac{2 (x) + 2 (1)}{17}$

Step 2.1.3

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

$- \frac{7 x}{16} - \frac{25}{12} = - 4 - \frac{2 (x + 1)}{17}$

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$- \frac{7 x}{16} - \frac{25}{12} = - 4 \cdot \frac{17}{17} - \frac{2 (x + 1)}{17}$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $- 4$ and $\frac{17}{17}$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 4 \cdot 17}{17} - \frac{2 (x + 1)}{17}$

Step 2.3.2

Combine the numerators over the common denominator.

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 4 \cdot 17 - 2 (x + 1)}{17}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Factor $- 2$ out of $- 4 \cdot 17 - 2 (x + 1)$ .

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Step 2.4.1.1

Reorder $- 4 \cdot 17$ and $- 2 (x + 1)$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 2 (x + 1) - 4 \cdot 17}{17}$

Step 2.4.1.2

Factor $- 2$ out of $- 4 \cdot 17$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 2 (x + 1) - 2 (2 \cdot 17)}{17}$

Step 2.4.1.3

Factor $- 2$ out of $- 2 (x + 1) - 2 (2 \cdot 17)$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 2 (x + 1 + 2 \cdot 17)}{17}$

Step 2.4.2

Multiply $2$ by $17$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 2 (x + 1 + 34)}{17}$

Step 2.4.3

Add $1$ and $34$ .

$- \frac{7 x}{16} - \frac{25}{12} = \frac{- 2 (x + 35)}{17}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{7 x}{16} - \frac{25}{12} = - \frac{2 (x + 35)}{17}$

Step 3

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

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Step 3.1

Add $\frac{2 (x + 35)}{17}$ to both sides of the equation.

$- \frac{7 x}{16} - \frac{25}{12} + \frac{2 (x + 35)}{17} = 0$

Step 3.2

To write $- \frac{7 x}{16}$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$- \frac{7 x}{16} \cdot \frac{17}{17} + \frac{2 (x + 35)}{17} - \frac{25}{12} = 0$

Step 3.3

To write $\frac{2 (x + 35)}{17}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$- \frac{7 x}{16} \cdot \frac{17}{17} + \frac{2 (x + 35)}{17} \cdot \frac{16}{16} - \frac{25}{12} = 0$

Step 3.4

Write each expression with a common denominator of $272$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{7 x}{16}$ by $\frac{17}{17}$ .

$- \frac{7 x \cdot 17}{16 \cdot 17} + \frac{2 (x + 35)}{17} \cdot \frac{16}{16} - \frac{25}{12} = 0$

Step 3.4.2

Multiply $16$ by $17$ .

$- \frac{7 x \cdot 17}{272} + \frac{2 (x + 35)}{17} \cdot \frac{16}{16} - \frac{25}{12} = 0$

Step 3.4.3

Multiply $\frac{2 (x + 35)}{17}$ by $\frac{16}{16}$ .

$- \frac{7 x \cdot 17}{272} + \frac{2 (x + 35) \cdot 16}{17 \cdot 16} - \frac{25}{12} = 0$

Step 3.4.4

Multiply $17$ by $16$ .

$- \frac{7 x \cdot 17}{272} + \frac{2 (x + 35) \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 7 x \cdot 17 + 2 (x + 35) \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $17$ by $- 7$ .

$\frac{- 119 x + 2 (x + 35) \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6.2

Apply the distributive property.

$\frac{- 119 x + (2 x + 2 \cdot 35) \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6.3

Multiply $2$ by $35$ .

$\frac{- 119 x + (2 x + 70) \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6.4

Apply the distributive property.

$\frac{- 119 x + 2 x \cdot 16 + 70 \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6.5

Multiply $16$ by $2$ .

$\frac{- 119 x + 32 x + 70 \cdot 16}{272} - \frac{25}{12} = 0$

Step 3.6.6

Multiply $70$ by $16$ .

$\frac{- 119 x + 32 x + 1120}{272} - \frac{25}{12} = 0$

Step 3.6.7

Add $- 119 x$ and $32 x$ .

$\frac{- 87 x + 1120}{272} - \frac{25}{12} = 0$

Step 3.7

To write $\frac{- 87 x + 1120}{272}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 87 x + 1120}{272} \cdot \frac{3}{3} - \frac{25}{12} = 0$

Step 3.8

To write $- \frac{25}{12}$ as a fraction with a common denominator, multiply by $\frac{68}{68}$ .

$\frac{- 87 x + 1120}{272} \cdot \frac{3}{3} - \frac{25}{12} \cdot \frac{68}{68} = 0$

Step 3.9

Write each expression with a common denominator of $816$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.9.1

Multiply $\frac{- 87 x + 1120}{272}$ by $\frac{3}{3}$ .

$\frac{(- 87 x + 1120) \cdot 3}{272 \cdot 3} - \frac{25}{12} \cdot \frac{68}{68} = 0$

Step 3.9.2

Multiply $272$ by $3$ .

$\frac{(- 87 x + 1120) \cdot 3}{816} - \frac{25}{12} \cdot \frac{68}{68} = 0$

Step 3.9.3

Multiply $\frac{25}{12}$ by $\frac{68}{68}$ .

$\frac{(- 87 x + 1120) \cdot 3}{816} - \frac{25 \cdot 68}{12 \cdot 68} = 0$

Step 3.9.4

Multiply $12$ by $68$ .

$\frac{(- 87 x + 1120) \cdot 3}{816} - \frac{25 \cdot 68}{816} = 0$

Step 3.10

Combine the numerators over the common denominator.

$\frac{(- 87 x + 1120) \cdot 3 - 25 \cdot 68}{816} = 0$

Step 3.11

Simplify the numerator.

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Step 3.11.1

Apply the distributive property.

$\frac{- 87 x \cdot 3 + 1120 \cdot 3 - 25 \cdot 68}{816} = 0$

Step 3.11.2

Multiply $3$ by $- 87$ .

$\frac{- 261 x + 1120 \cdot 3 - 25 \cdot 68}{816} = 0$

Step 3.11.3

Multiply $1120$ by $3$ .

$\frac{- 261 x + 3360 - 25 \cdot 68}{816} = 0$

Step 3.11.4

Multiply $- 25$ by $68$ .

$\frac{- 261 x + 3360 - 1700}{816} = 0$

Step 3.11.5

Subtract $1700$ from $3360$ .

$\frac{- 261 x + 1660}{816} = 0$

Step 3.12

Factor $- 1$ out of $- 261 x$ .

$\frac{- (261 x) + 1660}{816} = 0$

Step 3.13

Rewrite $1660$ as $- 1 (- 1660)$ .

$\frac{- (261 x) - 1 (- 1660)}{816} = 0$

Step 3.14

Factor $- 1$ out of $- (261 x) - 1 (- 1660)$ .

$\frac{- (261 x - 1660)}{816} = 0$

Step 3.15

Rewrite $- (261 x - 1660)$ as $- 1 (261 x - 1660)$ .

$\frac{- 1 (261 x - 1660)}{816} = 0$

Step 3.16

Move the negative in front of the fraction.

$- \frac{261 x - 1660}{816} = 0$

Step 4

Set the numerator equal to zero.

$261 x - 1660 = 0$

Step 5

Solve the equation for $x$ .

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Step 5.1

Add $1660$ to both sides of the equation.

$261 x = 1660$

Step 5.2

Divide each term in $261 x = 1660$ by $261$ and simplify.

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Step 5.2.1

Divide each term in $261 x = 1660$ by $261$ .

$\frac{261 x}{261} = \frac{1660}{261}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $261$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{261 x}{261} = \frac{1660}{261}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1660}{261}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1660}{261}$

Decimal Form:

$x = 6.36015325 \dots$

Mixed Number Form:

$x = 6 \frac{94}{261}$