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How do you solve the equation #4-absx=3#?

Answer 1

Ethan Adkins

#x = 1, –1#

Start by subtracting 4 from both sides to get:

#– |x| = –1 #

Multiply both sides by –1

#|x| = 1#

Eliminate the absolute value to get the solutions

#x = 1 and –x = 1#

divide the second equation by #–1# to get the second solution: #x = –1#

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Answer 2

Isaiah Anthony

To solve the equation (4 - |x| = 3), follow these steps:

Subtract 4 from both sides to isolate the absolute value term: (4 - 4 - |x| = 3 - 4), which simplifies to (-|x| = -1).
Divide both sides by (-1): (-|x| / (-1) = -1 / (-1)), yielding (|x| = 1).
Since the absolute value of a number can be either positive or negative, set up two separate equations for the cases when (x) is positive and when (x) is negative:
- For the case when (x) is positive, the equation becomes (x = 1).
- For the case when (x) is negative, the equation becomes (-x = 1).
Solve each equation separately:
- For (x = 1), no further steps are needed.
- For (-x = 1), multiply both sides by (-1) to solve for (x): (x = -1).
Combine the solutions from both cases: (x = 1) or (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.