Bunuel wrote:
Is x > 0 ?
(1) |x - 5| = 7x - 11
(2) |x + 5| = |x - 9|
Bunuel uses some great number sense to solve this question.
Here's a more traditional approach....
Target question: Is x > 0 ? Statement 1: |x - 5| = 7x - 11There 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
So, for the equation |x - 5| = 7x - 11, we must examine two cases:
Case a: x - 5 = 7x - 11. Solve to get x = 1. However, when we plug x = 1 into the original equation and simplify we get |-4| = -4, which is not true. So, x = 1 is NOT a solution
Case b: x - 5 = -(7x - 11). Solve to get x = 2. When we plug x = 2 into the original equation and simplify we get |-3| = 3, which is true. So, x = 2 is a solution.
So, the answer to the target question is
YES, x is positiveSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: |x + 5| = |x - 9|Once again we must solve two equations...
Case a: x + 5 = x - 9. This equation has no solution
Case b: x + 5 = -(x - 9). Solve to get x = 2
(we already learned in statement 1 that x = 2 satisfies the original equation. So, we need not confirm this again) So, the answer to the target question is
YES, x is positiveSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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