Solve for x |2x-6|=|x-3|

$| 2 x - 6 | = | x - 3 |$

Rewrite the equation as $| x - 3 | = | 2 x - 6 |$ .

$| x - 3 | = | 2 x - 6 |$

Rewrite the absolute value equation as four equations without absolute value bars.

$x - 3 = 2 x - 6$

$x - 3 = - (2 x - 6)$

$- (x - 3) = 2 x - 6$

$- (x - 3) = - (2 x - 6)$

After simplifying, there are only two unique equations to be solved.

$x - 3 = 2 x - 6$

$x - 3 = - (2 x - 6)$

Solve $x - 3 = 2 x - 6$ for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$x - 3 - 2 x = - 6$

Subtract $2 x$ from $x$ .

$- x - 3 = - 6$

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

Add $3$ to both sides of the equation.

$- x = - 6 + 3$

Add $- 6$ and $3$ .

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

List all of the solutions.

$x = 3, 3$