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How do you solve #abs(x-8)<=5#?

Answer 1

#3<=x<=13#

#x-8<=5# or #x<=8+5# or #x<=13#

Now consider #x-8>=-5# or #x>=8-5# or #x>=3# Therefore The value of #x# lies between #3# and #13# including #3# and #13# So we can write #3<=x<=13#

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Answer 2

Kennedy Adams

To solve the inequality abs(x - 8) ≤ 5, you consider two cases:

If (x - 8) is positive or zero, then abs(x - 8) = (x - 8).
If (x - 8) is negative, then abs(x - 8) = -(x - 8).

For case 1: (x - 8) ≤ 5 => x - 8 ≤ 5 => x ≤ 13

For case 2: -(x - 8) ≤ 5 => -x + 8 ≤ 5 => -x ≤ -3 => x ≥ 3

Combining the solutions from both cases: 3 ≤ x ≤ 13

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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 #abs(x-8)&lt;=5#?

How do you solve #abs(x-8)<=5#?