Solve for x (8x-10)/(13x-2x)=2/2

$\frac{8 x - 10}{13 x - 2 x} = \frac{2}{2}$

Factor each term.

Factor $2$ out of $8 x - 10$ .

Factor $2$ out of $8 x$ .

$\frac{2 (4 x) - 10}{13 x - 2 x} = \frac{2}{2}$

Factor $2$ out of $- 10$ .

$\frac{2 (4 x) + 2 (- 5)}{13 x - 2 x} = \frac{2}{2}$

Factor $2$ out of $2 (4 x) + 2 (- 5)$ .

$\frac{2 (4 x - 5)}{13 x - 2 x} = \frac{2}{2}$

Subtract $2 x$ from $13 x$ .

$\frac{2 (4 x - 5)}{11 x} = \frac{2}{2}$

Divide $2$ by $2$ .

$\frac{2 (4 x - 5)}{11 x} = 1$

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.

$11 x, 1$

The LCM of one and any expression is the expression.

$11 x$

Multiply each term in $\frac{2 (4 x - 5)}{11 x} = 1$ by $11 x$ to eliminate the fractions.

Multiply each term in $\frac{2 (4 x - 5)}{11 x} = 1$ by $11 x$ .

$\frac{2 (4 x - 5)}{11 x} (11 x) = 1 (11 x)$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$11 \frac{2 (4 x - 5)}{11 x} x = 1 (11 x)$

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$11 \frac{2 (4 x - 5)}{11 (x)} x = 1 (11 x)$

Cancel the common factor.

$11 \frac{2 (4 x - 5)}{11 x} x = 1 (11 x)$

Rewrite the expression.

$\frac{2 (4 x - 5)}{x} x = 1 (11 x)$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 (4 x - 5)}{x} x = 1 (11 x)$

Rewrite the expression.

$2 (4 x - 5) = 1 (11 x)$

Apply the distributive property.

$2 (4 x) + 2 \cdot - 5 = 1 (11 x)$

Multiply.

Multiply $4$ by $2$ .

$8 x + 2 \cdot - 5 = 1 (11 x)$

Multiply $2$ by $- 5$ .

$8 x - 10 = 1 (11 x)$

Simplify the right side.

Multiply $11 x$ by $1$ .

$8 x - 10 = 11 x$

Solve the equation.

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

Subtract $11 x$ from both sides of the equation.

$8 x - 10 - 11 x = 0$

Subtract $11 x$ from $8 x$ .

$- 3 x - 10 = 0$

Add $10$ to both sides of the equation.

$- 3 x = 10$

Divide each term in $- 3 x = 10$ by $- 3$ and simplify.

Divide each term in $- 3 x = 10$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{10}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{10}{- 3}$

Divide $x$ by $1$ .

$x = \frac{10}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{10}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{10}{3}$

Decimal Form:

$x = - 3.\overline{3}$

Mixed Number Form:

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

Solve for x (8x-10)/(13x-2x)=2/2

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