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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