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How do you solve #absx<2.5#?

Answer 1

Julia Adams

#-2.5< x<2.5#

#"the solution is going to be all the values that are"# #"less than 2.5 units away from zero"#

#"noting that "|-2|=|2|=2#

#-2.5< x<2.5" is the solution"#

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Answer 2

Isaiah Anthony

To solve the inequality |x| < 2.5, you need to consider two cases: when x is positive and when x is negative. Case 1: x > 0 In this case, the absolute value of x is simply x itself. So the inequality becomes x < 2.5. Case 2: x < 0 In this case, the absolute value of x is -x. So the inequality becomes -x < 2.5. To solve -x < 2.5, you multiply both sides by -1 to change the direction of the inequality, resulting in x > -2.5. Therefore, the solution to the inequality |x| < 2.5 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;2.5#?

How do you solve #absx<2.5#?