How many cases do you have after you remove the absolute value?
Solutions: x=5 and x=- 3 Number Line:
Practice makes perfect
An absolute value measures an expression's distance from a midpoint on a number line.
|x-1|= 4
This equation means that the distance is 4, either in the positive direction or the negative direction.
|x-1|= 4 ⇒ lx-1= 4 x-1= - 4
To find the solutions to the absolute value equation, we need to solve both of these cases for x.
| x-1|=4
lc x-1 ≥ 0:x-1 = 4 & (I) x-1 < 0:x-1 = - 4 & (II)
lcx-1=4 & (I) x-1=- 4 & (II)
(I), (II): LHS+1=RHS+1
lx_1=5 x_2=- 3
Both 5 and - 3 are solutions to the absolute value equation. Let's graph these solutions on a number line.
