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How do you solve the absolute value inequality and express the solution set in interval notation for #-2abs(s-3)<-4#?

Answer 1

Multiplying both sides of an inequality by a negative value reverses the inequality So #-2abs(s-3) < -4# is equivalent to #abs(s-3) > 2#

If #(s-3)# is negative (i.e. #s<3#) then this becomes #3-s > 2# #-s>-1# #s<1#

If #(s-3)# is positive or zero (i.e. #s>=3#) then #(s-3)>2# #s>5#

So #s epsilon (-oo,1)uuu(5,+oo)#

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Answer 2

Kennedy Adams

To solve the absolute value inequality -2|s - 3| < -4 and express the solution set in interval notation, you would first isolate the absolute value expression, then solve for the variable, and finally represent the solution set using interval notation. The solution set in interval notation is (-∞, 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 the absolute value inequality and express the solution set in interval notation for #-2abs(s-3)&lt;-4#?

How do you solve the absolute value inequality and express the solution set in interval notation for #-2abs(s-3)<-4#?