Algebra Examples

$\frac{7 + x}{x} = 22$

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.

$x, 1$

Step 1.2

The LCM of one and any expression is the expression.

$x$

Step 2

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

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Step 2.1

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

$\frac{7 + x}{x} x = 22 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 + x}{x} x = 22 x$

Step 2.2.1.2

Rewrite the expression.

$7 + x = 22 x$

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 $22 x$ from both sides of the equation.

$7 + x - 22 x = 0$

Step 3.1.2

Subtract $22 x$ from $x$ .

$7 - 21 x = 0$

Step 3.2

Subtract $7$ from both sides of the equation.

$- 21 x = - 7$

Step 3.3

Divide each term in $- 21 x = - 7$ by $- 21$ and simplify.

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Step 3.3.1

Divide each term in $- 21 x = - 7$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 21$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 21}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $- 7$ and $- 21$ .

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Step 3.3.3.1.1

Factor $- 7$ out of $- 7$ .

$x = \frac{- 7 (1)}{- 21}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $- 7$ out of $- 21$ .

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

$x = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$