Finite Math Examples

$\frac{1}{9} \cdot (x - 27) - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1

Simplify $\frac{1}{9} \cdot (x - 27) - \frac{1}{4} \cdot (x - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{9} x + \frac{1}{9} \cdot - 27 - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1.1.2

Combine $\frac{1}{9}$ and $x$ .

$\frac{x}{9} + \frac{1}{9} \cdot - 27 - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1.1.3

Cancel the common factor of $9$ .

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Step 1.1.3.1

Factor $9$ out of $- 27$ .

$\frac{x}{9} + \frac{1}{9} \cdot (9 (- 3)) - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1.1.3.2

Cancel the common factor.

$\frac{x}{9} + \frac{1}{9} \cdot (9 \cdot - 3) - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1.1.3.3

Rewrite the expression.

$\frac{x}{9} - 3 - \frac{1}{4} \cdot (x - 4) = x + 6$

Step 1.1.4

Apply the distributive property.

$\frac{x}{9} - 3 - \frac{1}{4} x - \frac{1}{4} \cdot - 4 = x + 6$

Step 1.1.5

Combine $x$ and $\frac{1}{4}$ .

$\frac{x}{9} - 3 - \frac{x}{4} - \frac{1}{4} \cdot - 4 = x + 6$

Step 1.1.6

Cancel the common factor of $4$ .

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Step 1.1.6.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{x}{9} - 3 - \frac{x}{4} + \frac{- 1}{4} \cdot - 4 = x + 6$

Step 1.1.6.2

Factor $4$ out of $- 4$ .

$\frac{x}{9} - 3 - \frac{x}{4} + \frac{- 1}{4} \cdot (4 (- 1)) = x + 6$

Step 1.1.6.3

Cancel the common factor.

$\frac{x}{9} - 3 - \frac{x}{4} + \frac{- 1}{4} \cdot (4 \cdot - 1) = x + 6$

Step 1.1.6.4

Rewrite the expression.

$\frac{x}{9} - 3 - \frac{x}{4} - 1 \cdot - 1 = x + 6$

Step 1.1.7

Multiply $- 1$ by $- 1$ .

$\frac{x}{9} - 3 - \frac{x}{4} + 1 = x + 6$

Step 1.2

To write $\frac{x}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{9} \cdot \frac{4}{4} - \frac{x}{4} - 3 + 1 = x + 6$

Step 1.3

To write $- \frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x}{9} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{9}{9} - 3 + 1 = x + 6$

Step 1.4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{x}{9}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{9 \cdot 4} - \frac{x}{4} \cdot \frac{9}{9} - 3 + 1 = x + 6$

Step 1.4.2

Multiply $9$ by $4$ .

$\frac{x \cdot 4}{36} - \frac{x}{4} \cdot \frac{9}{9} - 3 + 1 = x + 6$

Step 1.4.3

Multiply $\frac{x}{4}$ by $\frac{9}{9}$ .

$\frac{x \cdot 4}{36} - \frac{x \cdot 9}{4 \cdot 9} - 3 + 1 = x + 6$

Step 1.4.4

Multiply $4$ by $9$ .

$\frac{x \cdot 4}{36} - \frac{x \cdot 9}{36} - 3 + 1 = x + 6$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 9}{36} - 3 + 1 = x + 6$

Step 1.6

Find the common denominator.

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Step 1.6.1

Write $- 3$ as a fraction with denominator $1$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3}{1} + 1 = x + 6$

Step 1.6.2

Multiply $\frac{- 3}{1}$ by $\frac{36}{36}$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3}{1} \cdot \frac{36}{36} + 1 = x + 6$

Step 1.6.3

Multiply $\frac{- 3}{1}$ by $\frac{36}{36}$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3 \cdot 36}{36} + 1 = x + 6$

Step 1.6.4

Write $1$ as a fraction with denominator $1$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3 \cdot 36}{36} + \frac{1}{1} = x + 6$

Step 1.6.5

Multiply $\frac{1}{1}$ by $\frac{36}{36}$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3 \cdot 36}{36} + \frac{1}{1} \cdot \frac{36}{36} = x + 6$

Step 1.6.6

Multiply $\frac{1}{1}$ by $\frac{36}{36}$ .

$\frac{x \cdot 4 - x \cdot 9}{36} + \frac{- 3 \cdot 36}{36} + \frac{36}{36} = x + 6$

Step 1.7

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 9 - 3 \cdot 36 + 36}{36} = x + 6$

Step 1.8

Simplify each term.

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Step 1.8.1

Move $4$ to the left of $x$ .

$\frac{4 \cdot x - x \cdot 9 - 3 \cdot 36 + 36}{36} = x + 6$

Step 1.8.2

Multiply $9$ by $- 1$ .

$\frac{4 x - 9 x - 3 \cdot 36 + 36}{36} = x + 6$

Step 1.8.3

Multiply $- 3$ by $36$ .

$\frac{4 x - 9 x - 108 + 36}{36} = x + 6$

Step 1.9

Simplify terms.

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Step 1.9.1

Subtract $9 x$ from $4 x$ .

$\frac{- 5 x - 108 + 36}{36} = x + 6$

Step 1.9.2

Add $- 108$ and $36$ .

$\frac{- 5 x - 72}{36} = x + 6$

Step 1.9.3

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 72}{36} = x + 6$

Step 1.9.4

Rewrite $- 72$ as $- 1 (72)$ .

$\frac{- (5 x) - 1 (72)}{36} = x + 6$

Step 1.9.5

Factor $- 1$ out of $- (5 x) - 1 (72)$ .

$\frac{- (5 x + 72)}{36} = x + 6$

Step 1.9.6

Simplify the expression.

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Step 1.9.6.1

Rewrite $- (5 x + 72)$ as $- 1 (5 x + 72)$ .

$\frac{- 1 (5 x + 72)}{36} = x + 6$

Step 1.9.6.2

Move the negative in front of the fraction.

$- \frac{5 x + 72}{36} = x + 6$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$- \frac{5 x + 72}{36} - x = 6$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$- \frac{5 x + 72}{36} - x \cdot \frac{36}{36} = 6$

Step 2.3

Combine $- x$ and $\frac{36}{36}$ .

$- \frac{5 x + 72}{36} + \frac{- x \cdot 36}{36} = 6$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- (5 x + 72) - x \cdot 36}{36} = 6$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{- (5 x) - 1 \cdot 72 - x \cdot 36}{36} = 6$

Step 2.5.2

Multiply $5$ by $- 1$ .

$\frac{- 5 x - 1 \cdot 72 - x \cdot 36}{36} = 6$

Step 2.5.3

Multiply $- 1$ by $72$ .

$\frac{- 5 x - 72 - x \cdot 36}{36} = 6$

Step 2.5.4

Multiply $36$ by $- 1$ .

$\frac{- 5 x - 72 - 36 x}{36} = 6$

Step 2.5.5

Subtract $36 x$ from $- 5 x$ .

$\frac{- 41 x - 72}{36} = 6$

Step 2.6

Factor $- 1$ out of $- 41 x$ .

$\frac{- (41 x) - 72}{36} = 6$

Step 2.7

Rewrite $- 72$ as $- 1 (72)$ .

$\frac{- (41 x) - 1 (72)}{36} = 6$

Step 2.8

Factor $- 1$ out of $- (41 x) - 1 (72)$ .

$\frac{- (41 x + 72)}{36} = 6$

Step 2.9

Rewrite $- (41 x + 72)$ as $- 1 (41 x + 72)$ .

$\frac{- 1 (41 x + 72)}{36} = 6$

Step 2.10

Move the negative in front of the fraction.

$- \frac{41 x + 72}{36} = 6$

Step 3

Multiply both sides of the equation by $- 36$ .

$- 36 (- \frac{41 x + 72}{36}) = - 36 \cdot 6$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 36 (- \frac{41 x + 72}{36})$ .

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Step 4.1.1.1

Cancel the common factor of $36$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{41 x + 72}{36}$ into the numerator.

$- 36 \frac{- (41 x + 72)}{36} = - 36 \cdot 6$

Step 4.1.1.1.2

Factor $36$ out of $- 36$ .

$36 (- 1) \frac{- (41 x + 72)}{36} = - 36 \cdot 6$

Step 4.1.1.1.3

Cancel the common factor.

$36 \cdot - 1 \frac{- (41 x + 72)}{36} = - 36 \cdot 6$

Step 4.1.1.1.4

Rewrite the expression.

$- - (41 x + 72) = - 36 \cdot 6$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (41 x + 72) = - 36 \cdot 6$

Step 4.1.1.2.2

Multiply $41 x + 72$ by $1$ .

$41 x + 72 = - 36 \cdot 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 36$ by $6$ .

$41 x + 72 = - 216$

Step 5

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

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Step 5.1

Subtract $72$ from both sides of the equation.

$41 x = - 216 - 72$

Step 5.2

Subtract $72$ from $- 216$ .

$41 x = - 288$

Step 6

Divide each term in $41 x = - 288$ by $41$ and simplify.

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Step 6.1

Divide each term in $41 x = - 288$ by $41$ .

$\frac{41 x}{41} = \frac{- 288}{41}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $41$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{41 x}{41} = \frac{- 288}{41}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 288}{41}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{288}{41}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{288}{41}$

Decimal Form:

$x = - 7.\overline{02439}$

Mixed Number Form:

$x = - 7 \frac{1}{41}$