Calculus Examples

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

Step 1

Multiply $- \frac{5}{x + 2} \cdot \frac{2}{3}$ .

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Step 1.1

Multiply $\frac{2}{3}$ by $\frac{5}{x + 2}$ .

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

Step 1.2

Multiply $2$ by $5$ .

$- \frac{10}{3 (x + 2)} = 12$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$3 (x + 2), 1$

Step 2.2

The LCM of one and any expression is the expression.

$3 (x + 2)$

Step 3

Multiply each term in $- \frac{10}{3 (x + 2)} = 12$ by $3 (x + 2)$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{10}{3 (x + 2)} = 12$ by $3 (x + 2)$ .

$- \frac{10}{3 (x + 2)} (3 (x + 2)) = 12 (3 (x + 2))$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3 (x + 2)$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{10}{3 (x + 2)}$ into the numerator.

$\frac{- 10}{3 (x + 2)} (3 (x + 2)) = 12 (3 (x + 2))$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 10}{3 (x + 2)} (3 (x + 2)) = 12 (3 (x + 2))$

Step 3.2.1.3

Rewrite the expression.

$- 10 = 12 (3 (x + 2))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$- 10 = 12 (3 x + 3 \cdot 2)$

Step 3.3.2

Multiply $3$ by $2$ .

$- 10 = 12 (3 x + 6)$

Step 3.3.3

Apply the distributive property.

$- 10 = 12 (3 x) + 12 \cdot 6$

Step 3.3.4

Multiply.

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Step 3.3.4.1

Multiply $3$ by $12$ .

$- 10 = 36 x + 12 \cdot 6$

Step 3.3.4.2

Multiply $12$ by $6$ .

$- 10 = 36 x + 72$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $36 x + 72 = - 10$ .

$36 x + 72 = - 10$

Step 4.2

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

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Step 4.2.1

Subtract $72$ from both sides of the equation.

$36 x = - 10 - 72$

Step 4.2.2

Subtract $72$ from $- 10$ .

$36 x = - 82$

Step 4.3

Divide each term in $36 x = - 82$ by $36$ and simplify.

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Step 4.3.1

Divide each term in $36 x = - 82$ by $36$ .

$\frac{36 x}{36} = \frac{- 82}{36}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $36$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{36 x}{36} = \frac{- 82}{36}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 82}{36}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $- 82$ and $36$ .

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Step 4.3.3.1.1

Factor $2$ out of $- 82$ .

$x = \frac{2 (- 41)}{36}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $2$ out of $36$ .

$x = \frac{2 \cdot - 41}{2 \cdot 18}$

Step 4.3.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 41}{2 \cdot 18}$

Step 4.3.3.1.2.3

Rewrite the expression.

$x = \frac{- 41}{18}$

Step 4.3.3.2

Move the negative in front of the fraction.

$x = - \frac{41}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{41}{18}$

Decimal Form:

$x = - 2.2\overline{7}$

Mixed Number Form:

$x = - 2 \frac{5}{18}$