Algebra Examples

$6 + \frac{1}{x + 4} = 5$

Step 1

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

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Step 1.1

Subtract $6$ from both sides of the equation.

$\frac{1}{x + 4} = 5 - 6$

Step 1.2

Subtract $6$ from $5$ .

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

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.

$x + 4, 1$

Step 2.2

Remove parentheses.

$x + 4, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x + 4$

Step 3

Multiply each term in $\frac{1}{x + 4} = - 1$ by $x + 4$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{x + 4} = - 1$ by $x + 4$ .

$\frac{1}{x + 4} (x + 4) = - (x + 4)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x + 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{x + 4} (x + 4) = - (x + 4)$

Step 3.2.1.2

Rewrite the expression.

$1 = - (x + 4)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$1 = - x - 1 \cdot 4$

Step 3.3.2

Multiply $- 1$ by $4$ .

$1 = - x - 4$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- x - 4 = 1$ .

$- x - 4 = 1$

Step 4.2

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

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Step 4.2.1

Add $4$ to both sides of the equation.

$- x = 1 + 4$

Step 4.2.2

Add $1$ and $4$ .

$- x = 5$

Step 4.3

Divide each term in $- x = 5$ by $- 1$ and simplify.

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Step 4.3.1

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Step 4.3.2.2

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $5$ by $- 1$ .

$x = - 5$