|4r-12| if r<3
if r<3, then 4r-12 < 0
so |4r-12| = 12-4r
Well, |4r-12| is the absolute value of 4r-12. So if r<3, we can substitute r with its maximum value, which is 3. Then we have |4(3)-12| = |-12| = 12. So the value of |4r-12| when r<3 is 12. Now that's absolute-ly funny!
When solving absolute value inequalities, we need to consider two cases:
If r is greater than or equal to 3, then the expression |4r-12| remains unchanged.
If r is less than 3, then we need to evaluate |4r-12| by substituting the value of r into the expression.
Since r<3 in this case, we can substitute r = 3 into the expression |4r-12|:
|4(3)-12| = |12-12| = |0| = 0.
Therefore, if r is less than 3, the value of |4r-12| is 0.
To find the value of |4r-12| when r<3, we can follow these steps:
Step 1: Substitute the given condition r<3 into the expression |4r-12|.
|4r-12| = |4(3)-12| [Substituting r = 3 into |4r-12|]
= |12-12| [Simplifying]
= |0| [Simplifying further]
Step 2: Evaluate the absolute value of 0.
|0| = 0 [The absolute value of 0 is always 0]
Therefore, when r<3, the value of |4r-12| is 0.