Algebra Examples

$\frac{12 x}{4} - 9 (2 + x) + 18 = 36$

Step 1

Simplify $\frac{12 x}{4} - 9 (2 + x) + 18$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $- 9 (2 + x)$ as a fraction with denominator $1$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x)}{1} + 18 = 36$

Step 1.1.2

Multiply $\frac{- 9 (2 + x)}{1}$ by $\frac{4}{4}$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x)}{1} \cdot \frac{4}{4} + 18 = 36$

Step 1.1.3

Multiply $\frac{- 9 (2 + x)}{1}$ by $\frac{4}{4}$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x) \cdot 4}{4} + 18 = 36$

Step 1.1.4

Write $18$ as a fraction with denominator $1$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x) \cdot 4}{4} + \frac{18}{1} = 36$

Step 1.1.5

Multiply $\frac{18}{1}$ by $\frac{4}{4}$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x) \cdot 4}{4} + \frac{18}{1} \cdot \frac{4}{4} = 36$

Step 1.1.6

Multiply $\frac{18}{1}$ by $\frac{4}{4}$ .

$\frac{12 x}{4} + \frac{- 9 (2 + x) \cdot 4}{4} + \frac{18 \cdot 4}{4} = 36$

Step 1.2

Combine the numerators over the common denominator.

$\frac{12 x - 9 (2 + x) \cdot 4 + 18 \cdot 4}{4} = 36$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$\frac{12 x + (- 9 \cdot 2 - 9 x) \cdot 4 + 18 \cdot 4}{4} = 36$

Step 1.3.2

Multiply $- 9$ by $2$ .

$\frac{12 x + (- 18 - 9 x) \cdot 4 + 18 \cdot 4}{4} = 36$

Step 1.3.3

Apply the distributive property.

$\frac{12 x - 18 \cdot 4 - 9 x \cdot 4 + 18 \cdot 4}{4} = 36$

Step 1.3.4

Multiply $- 18$ by $4$ .

$\frac{12 x - 72 - 9 x \cdot 4 + 18 \cdot 4}{4} = 36$

Step 1.3.5

Multiply $4$ by $- 9$ .

$\frac{12 x - 72 - 36 x + 18 \cdot 4}{4} = 36$

Step 1.3.6

Multiply $18$ by $4$ .

$\frac{12 x - 72 - 36 x + 72}{4} = 36$

Step 1.4

Simplify terms.

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Step 1.4.1

Combine the opposite terms in $12 x - 72 - 36 x + 72$ .

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Step 1.4.1.1

Add $- 72$ and $72$ .

$\frac{12 x - 36 x + 0}{4} = 36$

Step 1.4.1.2

Add $12 x - 36 x$ and $0$ .

$\frac{12 x - 36 x}{4} = 36$

Step 1.4.2

Subtract $36 x$ from $12 x$ .

$\frac{- 24 x}{4} = 36$

Step 1.4.3

Cancel the common factor of $- 24$ and $4$ .

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Step 1.4.3.1

Factor $4$ out of $- 24 x$ .

$\frac{4 (- 6 x)}{4} = 36$

Step 1.4.3.2

Cancel the common factors.

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Step 1.4.3.2.1

Factor $4$ out of $4$ .

$\frac{4 (- 6 x)}{4 (1)} = 36$

Step 1.4.3.2.2

Cancel the common factor.

$\frac{4 (- 6 x)}{4 \cdot 1} = 36$

Step 1.4.3.2.3

Rewrite the expression.

$\frac{- 6 x}{1} = 36$

Step 1.4.3.2.4

Divide $- 6 x$ by $1$ .

$- 6 x = 36$

Step 2

Divide each term in $- 6 x = 36$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 x = 36$ by $- 6$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $36$ by $- 6$ .

$x = - 6$