For the first statement you need to use the two case approach for absolute values.

|2x−1|=3x+6 means that: 3x+6 could equal 2x−1, in which case:

x=−7

or, 3x+6 could equal −(2x−1) in which case:

3x+6=−2x+1, so

5x=−5

and therefore:

x=−1

So with two possible values it would be very tempting to say that statement 1 is not sufficient, then recognize that while statement 2 is clearly not sufficient on its own, it eliminates x=−7as a possibility when you use the two statements together. But wait!

If you return to your work from statement 1 to plug your solutions back in for a quick logic test, you'll see that −7 is an extraneous solution: |2(−7)−1|=3(−7)+6

means that:

|−15|=−15

Which does not work, since the absolute value on the left means that the left-hand side will be POSITIVE 15, while the right is stuck at NEGATIVE 15. This is known as an extraneous solution, and is why the process for solving absolute values always includes the step "plug your solutions back into the equation to verify that they are valid." Here, since −7 is invalid, statement 1 guarantees that x=−1 is the sole solution, and statement 1 is therefore sufficient. The correct answer is A.

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