Basic Math Examples

$2 = - \frac{1}{w + 5}$

Step 1

Rewrite the equation as $- \frac{1}{w + 5} = 2$ .

$- \frac{1}{w + 5} = 2$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$w + 5, 1$

Step 2.2

Remove parentheses.

$w + 5, 1$

Step 2.3

The LCM of one and any expression is the expression.

$w + 5$

Step 3

Multiply each term in $- \frac{1}{w + 5} = 2$ by $w + 5$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $- \frac{1}{w + 5} = 2$ by $w + 5$ .

$- \frac{1}{w + 5} (w + 5) = 2 (w + 5)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $w + 5$ .

Tap for more steps...

Step 3.2.1.1

Move the leading negative in $- \frac{1}{w + 5}$ into the numerator.

$\frac{- 1}{w + 5} (w + 5) = 2 (w + 5)$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 1}{w + 5} (w + 5) = 2 (w + 5)$

Step 3.2.1.3

Rewrite the expression.

$- 1 = 2 (w + 5)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$- 1 = 2 w + 2 \cdot 5$

Step 3.3.2

Multiply $2$ by $5$ .

$- 1 = 2 w + 10$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

Rewrite the equation as $2 w + 10 = - 1$ .

$2 w + 10 = - 1$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $10$ from both sides of the equation.

$2 w = - 1 - 10$

Step 4.2.2

Subtract $10$ from $- 1$ .

$2 w = - 11$

Step 4.3

Divide each term in $2 w = - 11$ by $2$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $2 w = - 11$ by $2$ .

$\frac{2 w}{2} = \frac{- 11}{2}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 w}{2} = \frac{- 11}{2}$

Step 4.3.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 11}{2}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Move the negative in front of the fraction.

$w = - \frac{11}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{11}{2}$

Decimal Form:

$w = - 5.5$

Mixed Number Form:

$w = - 5 \frac{1}{2}$