This equation means that the distance is 3, either in the positive direction or the negative direction.
|x|= 3 ⇒ lx= 3 x= - 3
Both 3 and -3 are solutions to the absolute value equation.
Let's graph these solutions on a number line.
b An absolute value measures an expression's distance from a midpoint on a number line.
|x|= 0
This equation means that the distance is 0, either in the positive direction or the negative direction. However, notice that ± 0 ⇔ 0, which means we only have one solution.
|x|= 0 ⇒ x=0
Let's graph this on a number line.
c Before we can remove the absolute value equation, we have to isolate it.
Now we can remove the absolute value, which gives us a positive and a negative solution.
|x|= 4 ⇒ lx= 4 x= - 4
Both -4 and 4 are solutions to the absolute value equation. Let's graph these solutions on a number line.
d Like in Part C, we have to isolate the absolute value before we can remove it.
Now we can remove the absolute value, which gives us a positive and a negative solution.
|x|= 5 ⇒ lx= 5 x= -5
Both -5 and 5 are solutions to the absolute value equation. Let's graph these solutions on a number line.
e Like in previous parts, if we remove the absolute value we get two equations.
|x-5|= 2 ⇒ lx-5= 2 x-5= - 2To find the solutions to the absolute value equation, we need to solve both of these cases for x.
