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How do you solve # |2x – 3| – 6 = –1#?

Answer 1

Hazel Anglin

#x = -1# or #x = 4#

# |2x – 3| – 6 = –1-> |2x – 3| =5#

we have two possibilities

1) # 2x – 3 =5->x = 4# 2) # 2x-3 =-5-> x =-1#

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Answer 2

Eva Adamson

First, isolate the absolute value expression:

[|2x - 3| - 6 = -1]

[|2x - 3| = 5]

Next, set up two equations to remove the absolute value (since (|a| = b) implies (a = b) or (a = -b)):

[2x - 3 = 5] and [2x - 3 = -5]

Solve each equation:

For (2x - 3 = 5): [2x = 8] [x = 4]

For (2x - 3 = -5): [2x = -2] [x = -1]

Therefore, the solutions are (x = 4) and (x = -1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.