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How do you solve #absx<1+abs1.5#?

Answer 1

Eva Abramson

Note that #abs(1.5) = 1.5# (taking the absolute value of a positive value has no effect on the value.

So #abs(x) <1 +abs(1.5)# is the same as #abs(x) < 2.5#

or #-2.5< x< 2.5#

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Answer 2

Savannah Anderson

To solve ( |x| < 1 + |1.5| ), you can follow these steps:

Simplify the expression inside the absolute value: ( |x| < 1 + 1.5 ) ( |x| < 2.5 )
Split the inequality into two cases: a) ( x < 2.5 ) b) ( x > -2.5 )

So, the solution set for ( |x| < 1 + |1.5| ) is ( -2.5 < x < 2.5 ).

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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 #absx&lt;1+abs1.5#?

How do you solve #absx<1+abs1.5#?