Algebra Examples

$\frac{4 x + 12}{2} = 3 x - 5$

Step 1

Cancel the common factor of $4 x + 12$ and $2$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) + 12}{2} = 3 x - 5$

Step 1.2

Factor $2$ out of $12$ .

$\frac{2 (2 x) + 2 \cdot 6}{2} = 3 x - 5$

Step 1.3

Factor $2$ out of $2 (2 x) + 2 (6)$ .

$\frac{2 (2 x + 6)}{2} = 3 x - 5$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $2$ .

$\frac{2 (2 x + 6)}{2 (1)} = 3 x - 5$

Step 1.4.2

Cancel the common factor.

$\frac{2 (2 x + 6)}{2 \cdot 1} = 3 x - 5$

Step 1.4.3

Rewrite the expression.

$\frac{2 x + 6}{1} = 3 x - 5$

Step 1.4.4

Divide $2 x + 6$ by $1$ .

$2 x + 6 = 3 x - 5$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $3 x$ from both sides of the equation.

$2 x + 6 - 3 x = - 5$

Step 2.1.2

Subtract $3 x$ from $2 x$ .

$- x + 6 = - 5$

Step 2.2

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

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$- x = - 5 - 6$

Step 2.2.2

Subtract $6$ from $- 5$ .

$- x = - 11$

Step 2.3

Divide each term in $- x = - 11$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- x = - 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 11$ by $- 1$ .

$x = 11$