Algebra Examples

$\frac{2}{3} (3 x + 9) = - 2 (2 x + 6)$

Step 1

Simplify $\frac{2}{3} \cdot (3 x + 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (3 x + 9) = - 2 (2 x + 6)$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (3 x + 9) = - 2 (2 x + 6)$

Step 1.3

Apply the distributive property.

$\frac{2}{3} (3 x) + \frac{2}{3} \cdot 9 = - 2 (2 x + 6)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $3 x$ .

$\frac{2}{3} (3 (x)) + \frac{2}{3} \cdot 9 = - 2 (2 x + 6)$

Step 1.4.2

Cancel the common factor.

$\frac{2}{3} (3 x) + \frac{2}{3} \cdot 9 = - 2 (2 x + 6)$

Step 1.4.3

Rewrite the expression.

$2 x + \frac{2}{3} \cdot 9 = - 2 (2 x + 6)$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $9$ .

$2 x + \frac{2}{3} \cdot (3 (3)) = - 2 (2 x + 6)$

Step 1.5.2

Cancel the common factor.

$2 x + \frac{2}{3} \cdot (3 \cdot 3) = - 2 (2 x + 6)$

Step 1.5.3

Rewrite the expression.

$2 x + 2 \cdot 3 = - 2 (2 x + 6)$

Step 1.6

Multiply $2$ by $3$ .

$2 x + 6 = - 2 (2 x + 6)$

Step 2

Simplify $- 2 (2 x + 6)$ .

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Step 2.1

Apply the distributive property.

$2 x + 6 = - 2 (2 x) - 2 \cdot 6$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $- 2$ .

$2 x + 6 = - 4 x - 2 \cdot 6$

Step 2.2.2

Multiply $- 2$ by $6$ .

$2 x + 6 = - 4 x - 12$

Step 3

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

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Step 3.1

Add $4 x$ to both sides of the equation.

$2 x + 6 + 4 x = - 12$

Step 3.2

Add $2 x$ and $4 x$ .

$6 x + 6 = - 12$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$6 x = - 12 - 6$

Step 4.2

Subtract $6$ from $- 12$ .

$6 x = - 18$

Step 5

Divide each term in $6 x = - 18$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 x = - 18$ by $6$ .

$\frac{6 x}{6} = \frac{- 18}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 18}{6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 18}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 18$ by $6$ .

$x = - 3$