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
