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Problem 706

AMC 10/12, early questions

Algebra Difficulty 3.9 Multiple choice Olimpiadi di Matematica · Italy

Two real numbers $a$ and $b$ are given such that $|3 a-b+1|=|b|$ . Then necessarily we have...

Pick one

Official solution

Solution:

The answer is (E). Indeed, in the Cartesian plane having axes $a$ and $b$ , the region described by the equation $|3 a-b+1|=|b|$ is given by the union of the line $3 a+1=0$ and the line $3 a-2 b+1=0$ . Therefore none of the first four proposed answers is correct.

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