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How do you solve #abs(2-x)>abs(x+1)#?

Answer 1

To solve this problem I started by substituting positive and negative numbers into the expression to get a sense of the answer. It is pretty clear most positive numbers would make the sentence false:

#if x = 100# then #98 < 101#

#if x=1# then #1<2#

Also it is clear negative numbers will make the statement true since #2 - (-x) = 2 + x#

#if x = -5# then #7>4#

To solve the inequality: #2-x > x+1# #1 > 2x# #0.5>x# #x<0.5#

This answer makes sense (one last check): #if x = 0.25# then #1.75 >1.25#

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Answer 2

Ethan Adkins

To solve the inequality abs(2-x) > abs(x+1), you need to consider the different cases when the expressions inside the absolute value bars are positive and negative.

Case 1: When both expressions are positive: 2 - x > x + 1

Case 2: When both expressions are negative: -(2 - x) > -(x + 1)

Case 3: When one expression is positive and the other is negative: 2 - x > -(x + 1) -(2 - x) > x + 1

Solve each inequality separately to find the values of x that satisfy the original inequality.

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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(2-x)&gt;abs(x+1)#?

How do you solve #abs(2-x)>abs(x+1)#?