Solve for x (x-2)/(2x-1)=-2

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

Step 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.

$2 x - 1, 1$

Remove parentheses.

$2 x - 1, 1$

The LCM of one and any expression is the expression.

$2 x - 1$

Step 2

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

Multiply each term in $\frac{x - 2}{2 x - 1} = - 2$ by $2 x - 1$ .

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

Simplify the left side.

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$x - 2 = - 2 (2 x - 1)$

Simplify the right side.

Apply the distributive property.

$x - 2 = - 2 (2 x) - 2 \cdot - 1$

Multiply.

Multiply $2$ by $- 2$ .

$x - 2 = - 4 x - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x - 2 = - 4 x + 2$

Step 3

Solve the equation.

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

Add $4 x$ to both sides of the equation.

$x - 2 + 4 x = 2$

Add $x$ and $4 x$ .

$5 x - 2 = 2$

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

Add $2$ to both sides of the equation.

$5 x = 2 + 2$

Add $2$ and $2$ .

$5 x = 4$

Divide each term in $5 x = 4$ by $5$ and simplify.

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$

Solve for x (x-2)/(2x-1)=-2

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