Ok. LAST math question, lol..?

Question

how would I do this?
|x-4|<(or less than)2

Answer 1

I see some people giving a wrong range of answers that includes, for example, 0. It's wrong because |0-4| = 4, which is not <= 2.

You know |x| is the same as x if x>=0, and |x| is -x if x<=0. So |x - 4| could mean x - 4 if x>=4, and -(x - 4) if x<=4. Set this up as two inequalities, solve them separately, and combine results at the end:

x - 4 <= 2, if x>=4
-(x - 4) <= 2, if x<=4

These become
x <= 6 if x >=4, which means 4 <= x <= 6
x >= 2 if x <=4, which means 2 <= x <= 4
Combing these give 2 <= x <= 6

Answer 2

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Answer 3

think of it as two equations
x-4=2 and x-4= -2
x=6 and x=2
plug the inequalities back in there
or draw a number line with points at
<--2----6---> test points, plug it into the equation
2 lessthan x lessthan 6

Answer 4

|x-4| < 2
Case 1: x-4 >0
x-4 < 2
x<6
Case 2: x-4 <0
|x-4| =-x-4
-x-4 < 2
-x<6
x > -6
case 3: x-4 =0 then x=4
so, combining all -6

Answer 5

|x-4|< 2

absolute value means

x-4<2 AND
x+4>2

so x<6 and x>-2 (algebra for above equations.

-2

Answer 6

the 2 ll means that it makes the answer positive iside of it. so x=3 or 4 or 5 or 6

Answer 7

|x-4) < 2 can be rewritten as:
-2 < x-4 < 2
Add 4 to each term
2 < x < 6