Pre-Algebra Examples

$\frac{2 x - 12}{x} = 5$

Step 1

Factor $2$ out of $2 x - 12$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $2 x$ .

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

Step 1.2

Factor $2$ out of $- 12$ .

$\frac{2 x + 2 \cdot - 6}{x} = 5$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot - 6$ .

$\frac{2 (x - 6)}{x} = 5$

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.

$x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{2 (x - 6)}{x} = 5$ by $x$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{2 (x - 6)}{x} = 5$ by $x$ .

$\frac{2 (x - 6)}{x} x = 5 x$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 (x - 6)}{x} x = 5 x$

Step 3.2.1.2

Rewrite the expression.

$2 (x - 6) = 5 x$

Step 3.2.2

Apply the distributive property.

$2 x + 2 \cdot - 6 = 5 x$

Step 3.2.3

Multiply $2$ by $- 6$ .

$2 x - 12 = 5 x$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $5 x$ from both sides of the equation.

$2 x - 12 - 5 x = 0$

Step 4.1.2

Subtract $5 x$ from $2 x$ .

$- 3 x - 12 = 0$

Step 4.2

Add $12$ to both sides of the equation.

$- 3 x = 12$

Step 4.3

Divide each term in $- 3 x = 12$ by $- 3$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $- 3 x = 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{- 3}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $12$ by $- 3$ .

$x = - 4$