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How do you solve the inequality #abs(x-3)<8#?

Answer 1

Genesis Allen

Solution: # -5 < x <11 # . In interval notation : #(-5 , 11)#

#| x- 3 | < 8 or x -3 < 8 or x < 11# OR

#| x- 3 | < 8 or x -3 > -8 or x > - 5#

Solution: # -5 < x <11 # . In interval notation: #(-5 , 11)# [Ans]

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Answer 2

Genesis Allen

To solve the inequality (|x - 3| < 8), you need to consider two cases:

When (x - 3) is positive: Solve (x - 3 < 8) for (x).
When (x - 3) is negative: Solve (-(x - 3) < 8) for (x).

After solving each case, combine the solutions to find the overall solution set for (x).

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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.

How do you solve the inequality #abs(x-3)&lt;8#?

How do you solve the inequality #abs(x-3)<8#?