How many cases do you have after you remove the absolute value?
Solutions: t=12 and t=- 12 Number Line:
Practice makes perfect
An absolute value measures an expression's distance from a midpoint on a number line.
|t/2|= 6
This equation means that the distance is 6, either in the positive direction or the negative direction.
t/2= 6 and t/2= - 6
To find the solutions to the absolute value equation, we need to solve both of these cases for t.
|t/2|=6
lc t2 ≥ 0: t2 = 6 & (I) t2 < 0: t2 = - 6 & (II)
lc t2=6 & (I) t2=-6 & (II)
(I), (II): LHS * 2=RHS* 2
lt_1=12 t_2=-12
Both 12 and - 12 are solutions to the absolute value equation. Let's graph these solutions on a number line.