An absolute value is always a non-negative number because it measures the expression's distance from a midpoint on a number line.
|x-3|= 6
This equation means that the distance is 6, either in the positive direction or the negative direction.
|x-3|= 6 ⇒ lx-3= 6 x-3= -6
We need to solve both of these cases so that we can find both values that satisfy the equation.
After solving an absolute value equation, it is necessary to check for extraneous solutions. To do this, we substitute the found solutions into the given equation and determine if a true statement is made.
Substituting 9 for x in the equation does result in a true statement, so x=9 is not an extraneous solution. Now let's check whether or not x=- 3 is extraneous.
Substituting (- 3) for x in the equation also does result in a true statement, so x=- 3 is not an extraneous solution. Therefore, the equation has two solutions.
