Solve for x (4x-10)/x=8

$\frac{4 x - 10}{x} = 8$

Step 1

Factor $2$ out of $4 x - 10$ .

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) - 10}{x} = 8$

Factor $2$ out of $- 10$ .

$\frac{2 (2 x) + 2 (- 5)}{x} = 8$

Factor $2$ out of $2 (2 x) + 2 (- 5)$ .

$\frac{2 (2 x - 5)}{x} = 8$

Step 2

Find the LCD of the terms in the equation.

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

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{2 (2 x - 5)}{x} = 8$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{2 (2 x - 5)}{x} = 8$ by $x$ .

$\frac{2 (2 x - 5)}{x} x = 8 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 (2 x - 5)}{x} x = 8 x$

Rewrite the expression.

$2 (2 x - 5) = 8 x$

Apply the distributive property.

$2 (2 x) + 2 \cdot - 5 = 8 x$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 5 = 8 x$

Multiply $2$ by $- 5$ .

$4 x - 10 = 8 x$

Step 4

Solve the equation.

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

Subtract $8 x$ from both sides of the equation.

$4 x - 10 - 8 x = 0$

Subtract $8 x$ from $4 x$ .

$- 4 x - 10 = 0$

Add $10$ to both sides of the equation.

$- 4 x = 10$

Divide each term in $- 4 x = 10$ by $- 4$ and simplify.

Divide each term in $- 4 x = 10$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{10}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{10}{- 4}$

Divide $x$ by $1$ .

$x = \frac{10}{- 4}$

Simplify the right side.

Cancel the common factor of $10$ and $- 4$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

$x = - 2 \frac{1}{2}$

Solve for x (4x-10)/x=8

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