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
Source: Kaplan

Take: |12 − 4x| + 2 = 6
Isolate the absolute value part by subtracting 2 from both sides of the inequality: |12 − 4x| = 4

NICE RULE: If |x| = k, then x = k or x = -k

We get: 12 − 4x = 4 or 12 − 4x = -4

If 12 − 4x = 4, then x = 2.
Check the answer choices....x = 2 is not an option. Keep going.

If 12 − 4x = -4, then x = 4
Check the answer choices....bingo!

Answer: E

Cheers,
Brent

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