Algebra Examples

$3 (4 x + 2) = 20 x - 9 x + 2$

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.

$20 x - 9 x + 2 = 3 (4 x + 2)$

Step 2

Subtract $9 x$ from $20 x$ .

$11 x + 2 = 3 (4 x + 2)$

Step 3

Simplify $3 (4 x + 2)$ .

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Step 3.1

Apply the distributive property.

$11 x + 2 = 3 (4 x) + 3 \cdot 2$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $4$ by $3$ .

$11 x + 2 = 12 x + 3 \cdot 2$

Step 3.2.2

Multiply $3$ by $2$ .

$11 x + 2 = 12 x + 6$

Step 4

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

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Step 4.1

Subtract $12 x$ from both sides of the equation.

$11 x + 2 - 12 x = 6$

Step 4.2

Subtract $12 x$ from $11 x$ .

$- x + 2 = 6$

Step 5

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

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Step 5.1

Subtract $2$ from both sides of the equation.

$- x = 6 - 2$

Step 5.2

Subtract $2$ from $6$ .

$- x = 4$

Step 6

Divide each term in $- x = 4$ by $- 1$ and simplify.

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Step 6.1

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Step 6.2.2

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $4$ by $- 1$ .

$x = - 4$