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How do you solve #abs(3-x )= 6#?

Answer 1

Hazel Anglin

In absolute value equations, there are two scenarios that you must consider and therefore there will be two solutions

Scenario 1: The absolute value is positive:

#3 - x = 6#

#-x = 3#

#x = -3#

Scenario 2: The absolute value is negative:

#-(3 - x) = 6#

#-3 + x = 6

#x = 9#

Always check your solutions in the original equation. Both solutions work, so the solution set is #{x = -3,9}#

Hopefully this helps.

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Answer 2

Savannah Anderson

To solve the equation abs(3-x) = 6, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (3-x \geq 0) (3 - x = 6) (x = 3 - 6) (x = -3)

Case 2: (3-x < 0) (-(3 - x) = 6) (x - 3 = 6) (x = 6 + 3) (x = 9)

So, the solutions are (x = -3) and (x = 9).

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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.