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How do you make #4x<16# or #8x>16# into an absolute inequality?

Answer 1

Simplest answer #abs(x) >= 0#

#4x < 16 rarr x < 4# #8x > 16 rarr x > 2#

#(4x < 16) or (8x > 16)# #harr (x<4) or (x>2)#

...but this is true for any Real value of #x#

It is possible (maybe, even likely, that the inequality signs where switched); a more reasonable question would have been "How do you make #4x > 16# or #8x <16# into an absolute value inequality?"

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Answer 2

Avery Alexander

To combine the inequalities \(4x < 16\) or \(8x > 16\) into an absolute inequality, you can use the logical operator "or" (represented by the symbol \(\lor\)). So, the combined absolute inequality would be: \[|4x| < 16 \lor |8x| > 16\]

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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 make #4x&lt;16# or #8x&gt;16# into an absolute inequality?

How do you make #4x<16# or #8x>16# into an absolute inequality?