Pre-Algebra Examples

$\frac{- 22 + 3 x}{3 x + 7} = 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 x + 7, 1$

Step 1.2

Remove parentheses.

$3 x + 7, 1$

Step 1.3

The LCM of one and any expression is the expression.

$3 x + 7$

Step 2

Multiply each term in $\frac{- 22 + 3 x}{3 x + 7} = 2$ by $3 x + 7$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{- 22 + 3 x}{3 x + 7} = 2$ by $3 x + 7$ .

$\frac{- 22 + 3 x}{3 x + 7} (3 x + 7) = 2 (3 x + 7)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3 x + 7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 22 + 3 x}{3 x + 7} (3 x + 7) = 2 (3 x + 7)$

Step 2.2.1.2

Rewrite the expression.

$- 22 + 3 x = 2 (3 x + 7)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$- 22 + 3 x = 2 (3 x) + 2 \cdot 7$

Step 2.3.2

Multiply.

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Step 2.3.2.1

Multiply $3$ by $2$ .

$- 22 + 3 x = 6 x + 2 \cdot 7$

Step 2.3.2.2

Multiply $2$ by $7$ .

$- 22 + 3 x = 6 x + 14$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Subtract $6 x$ from both sides of the equation.

$- 22 + 3 x - 6 x = 14$

Step 3.1.2

Subtract $6 x$ from $3 x$ .

$- 22 - 3 x = 14$

Step 3.2

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

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Step 3.2.1

Add $22$ to both sides of the equation.

$- 3 x = 14 + 22$

Step 3.2.2

Add $14$ and $22$ .

$- 3 x = 36$

Step 3.3

Divide each term in $- 3 x = 36$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $- 3 x = 36$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{36}{- 3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{36}{- 3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{- 3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $36$ by $- 3$ .

$x = - 12$