Algebra Examples

$2 (4 x + 2) = 4 x - 12 (x - 1)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x - 12 (x - 1) = 2 (4 x + 2)$

Step 2

Simplify $4 x - 12 (x - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 x - 12 x - 12 \cdot - 1 = 2 (4 x + 2)$

Step 2.1.2

Multiply $- 12$ by $- 1$ .

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

Step 2.2

Subtract $12 x$ from $4 x$ .

$- 8 x + 12 = 2 (4 x + 2)$

Step 3

Simplify $2 (4 x + 2)$ .

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Step 3.1

Apply the distributive property.

$- 8 x + 12 = 2 (4 x) + 2 \cdot 2$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $4$ by $2$ .

$- 8 x + 12 = 8 x + 2 \cdot 2$

Step 3.2.2

Multiply $2$ by $2$ .

$- 8 x + 12 = 8 x + 4$

Step 4

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

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Step 4.1

Subtract $8 x$ from both sides of the equation.

$- 8 x + 12 - 8 x = 4$

Step 4.2

Subtract $8 x$ from $- 8 x$ .

$- 16 x + 12 = 4$

Step 5

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

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Step 5.1

Subtract $12$ from both sides of the equation.

$- 16 x = 4 - 12$

Step 5.2

Subtract $12$ from $4$ .

$- 16 x = - 8$

Step 6

Divide each term in $- 16 x = - 8$ by $- 16$ and simplify.

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Step 6.1

Divide each term in $- 16 x = - 8$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{- 8}{- 16}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 16$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{- 8}{- 16}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 16}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 8$ and $- 16$ .

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Step 6.3.1.1

Factor $- 8$ out of $- 8$ .

$x = \frac{- 8 (1)}{- 16}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $- 8$ out of $- 16$ .

$x = \frac{- 8 \cdot 1}{- 8 \cdot 2}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{- 8 \cdot 1}{- 8 \cdot 2}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$