MathRevolution wrote:
[
Math Revolution GMAT math practice question]
If \(|x-6|=2x\), then \(x=?\)
\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)
There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says:
If |x| = k, then x = k or x = -k2. 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 =
-6Step 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 =
2Step 3: Plug solution into original equation to get: |(
2) - 6| = 2(
2)
Evaluate to get: |-4| = 4 WORK!
Answer: D
Cheers,
Brent
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