Problem Solving (PS) | Re: If x4, what is the range of the solutions of the equation |14x|=24/(

Hi @KarishmaB, 

In the 2nd case - Multiply both sides by (x-4) to get: (14–x)(x−4) = -24, upon solving the equation we received the values 16 and 2. However these are not negative values as per our assumption for the expression. Hence, shouldn't they be outright rejected instead of testing?

I am trying to understand the testing rationalehere.

BrentGMATPrepNow


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

Given: |14–x|=24/(x−4)

So, we need to check 14–x =24/(x−4) and 14–x =-24/(x−4)

14–x =24/(x−4)
Multiply both sides by (x-4) to get: (14–x)(x−4) = 24
Expand: -x² + 18x - 56 = 24
Rearrange to get: x² - 18x + 80 = 0
Factor: (x - 10)(x - 8) = 0
So, x = 10 or
...

Statistics : Posted by KarishmaB • on 28 Apr 2017, 02:04 • Replies 11 • Views 11195

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