Algebra Examples

$2.25 (4 x - 4) = - 2 + 10 x + 12$

Step 1

Simplify $2.25 (4 x - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2.25 (4 x - 4) = - 2 + 10 x + 12$

Step 1.2

Simplify by adding zeros.

$2.25 (4 x - 4) = - 2 + 10 x + 12$

Step 1.3

Apply the distributive property.

$2.25 (4 x) + 2.25 \cdot - 4 = - 2 + 10 x + 12$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $2.25$ .

$9 x + 2.25 \cdot - 4 = - 2 + 10 x + 12$

Step 1.4.2

Multiply $2.25$ by $- 4$ .

$9 x - 9 = - 2 + 10 x + 12$

Step 2

Add $- 2$ and $12$ .

$9 x - 9 = 10 x + 10$

Step 3

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

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Step 3.1

Subtract $10 x$ from both sides of the equation.

$9 x - 9 - 10 x = 10$

Step 3.2

Subtract $10 x$ from $9 x$ .

$- 1 x - 9 = 10$

Step 4

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

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Step 4.1

Add $9$ to both sides of the equation.

$- 1 x = 10 + 9$

Step 4.2

Add $10$ and $9$ .

$- 1 x = 19$

Step 5

Divide each term in $- 1 x = 19$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- 1 x = 19$ by $- 1$ .

$\frac{- 1 x}{- 1} = \frac{19}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 1$ .

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Step 5.2.1.1

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

$\frac{- 1 (1) x}{- 1} = \frac{19}{- 1}$

Step 5.2.1.2

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

$\frac{1 (- 1 \cdot 1 x)}{- 1} = \frac{19}{- 1}$

Step 5.2.1.3

Move the negative one from the denominator of $\frac{- 1 \cdot 1 x}{- 1}$ .

$- 1 \cdot (- 1 \cdot 1 x) = \frac{19}{- 1}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Rewrite $- 1 \cdot (- 1 \cdot 1 x)$ as $- (- 1 \cdot 1 x)$ .

$- (- 1 \cdot 1 x) = \frac{19}{- 1}$

Step 5.2.2.2

Multiply $- 1$ by $1$ .

$- (- 1 x) = \frac{19}{- 1}$

Step 5.2.2.3

Rewrite $- 1 x$ as $- x$ .

$- - x = \frac{19}{- 1}$

Step 5.2.3

Multiply $- - x$ .

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Step 5.2.3.1

Multiply $- 1$ by $- 1$ .

$1 x = \frac{19}{- 1}$

Step 5.2.3.2

Multiply $x$ by $1$ .

$x = \frac{19}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $19$ by $- 1$ .

$x = - 19$