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

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

Multiply both sides by $x - 2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $x - 2$ by $1$ .

$| x - 2 | = x - 2$

Solve for $x$ .

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 2 = \pm (x - 2)$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 2 = x - 2$

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

Subtract $x$ from both sides of the equation.

$x - 2 - x = - 2$

Combine the opposite terms in $x - 2 - x$ .

Subtract $x$ from $x$ .

$0 - 2 = - 2$

Subtract $2$ from $0$ .

$- 2 = - 2$

Since $- 2 = - 2$ , the equation will always be true.

All real numbers

Next, use the negative value of the $\pm$ to find the second solution.

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

Simplify $- (x - 2)$ .

Rewrite.

$x - 2 = 0 + 0 - (x - 2)$

Simplify by adding zeros.

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

Apply the distributive property.

$x - 2 = - x - - 2$

Multiply $- 1$ by $- 2$ .

$x - 2 = - x + 2$

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

Add $x$ to both sides of the equation.

$x - 2 + x = 2$

Add $x$ and $x$ .

$2 x - 2 = 2$

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

Add $2$ to both sides of the equation.

$2 x = 2 + 2$

Add $2$ and $2$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x =, 2$

Exclude the solutions that do not make $\frac{| x - 2 |}{x - 2} = 1$ true.

$No solution$

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

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