# Sum of x values in an absolute value equation

$$|x-3| \cdot |x-2|=|x-3|$$

How should I go about solving for x? Is there a intuitive method for solving these types of absolute value equations? I tried to plug in a 3 first:

$$|3-3| \cdot |3-2|=|3-3|$$

which ended up as

$$|0| \cdot |1|=|0| =0$$

But I don't know whether this is the way to go, whether I am doing this wrong or not so I hope someone could help me solve this.

Collect $|x-3|$ to obtain $$|x-3| \left( |x-2|-1 \right)=0$$ Now equate each factor to zero and find solutions $$x=3, x=1$$
• He means factorize, but you can as well have $x=3$ solution and when $x\neq 3$ divide each side by $|x-3|$, you end up with the same conclusion. – zwim Nov 14 '17 at 7:09