BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:29 am

If |x − 6| = 2x, then x = ?

A) −6
B) −4
C) 0
D) 2
E) 6
Answer: D
Source: Math Revolution

There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Step 1: x - 6 = 2x or x - 6 = -2x

case a: x - 6 = 2x
Step 2: Solve to get x = -6
Step 3: Plug solution into original equation to get: |(-6) - 6| = 2(-6)
Evaluate to get: |-12| = -12 DOESN'T WORK

case b: x - 6 = -2x
Step 2: Solve to get x = 2
Step 3: Plug solution into original equation to get: |(2) - 6| = 2(2)
Evaluate to get: |-4| = 4 WORKS!

Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:29 am

If |x − 6| = 2x, then x = ?

A) −6
B) −4
C) 0
D) 2
E) 6
Answer: D
Source: Math Revolution

For this absolute value question, we consider two cases, the first that (x - 6) is positive, and the second that (x - 6) is negative.

Case 1. If (x - 6) is positive, we have:

x - 6 = 2x

-6 = x

However, if we substitute -6 for x in the original equation, the left hand side of the equation is |-6 - 6| = |-12| = 12, but the right hand side is 2(-6) = -12. Thus, x can’t be -6.

Case 2. If (x - 6) is negative, we have:

-(x - 6) = 2x

-x + 6 = 2x

6 = 3x

2 = x

Answer: D