BTGModeratorVI wrote: ↑Thu Jun 11, 2020 8:34 am
Which of the following could be the value of x, if |12 − 4x| + 2 = 6?
A. −4
B. −2
C. 1
D. 3
E. 4
Answer:
E
Solution:
Looking at the choices, we see that if x = 4, we have |12 - 16| + 2 = |-4| + 2 = 4 + 2 = 6.
(Note: We can solve this equation algebraically; however, sometimes it’s easier to just substitute in the numbers.)
Alternate Solution:
Let’s do the algebraic solution. First, we re-express the equation as |12 − 4x| = 4
Now, recall that to solve an absolute value equation, we always have two cases, as shown below.
Case 1. Drop the absolute value signs and solve for x:
12 - 4x = 4
-4x = -8
x = 2
Case 2. Drop the absolute value signs and negate the expression. Then solve for x.
-(12 - 4x) = 4
-12 + 4x = 4
4x = 16
x = 4.
Of the two solutions x = 2 and x = 4, only x = 4 appears in the answer choices.
Answer: E
