Hi Kay;
In the title, you explain this is <.
In the description, you explain this is ≤.
I will use the first...
23x < 11
Absolute value is always positive.
(23x) can be either...
+(23x) or (23x).
When the absolute value of either is taken, it has the same result.
(23x)<11
2+3x<11
Let's add 2 to both sides...
2+2+3x<11+2
3x<13
Divide both sides by 3...
(3x)/3<13/3
x<13/3
+(23x)<11
23x<11
Let's subtract 2 from both sides...
223x<112
3x<9
Divide both sides by 3. Because this is a negative number < will switch to >...
(3x)/3>9/3
x>3
3<x<13/3
Let's verify by pluggingin a few points within this domain...
23x < 11
x=0
2[(3)(0)]<11
2<11
2<11YES
x=1
23x < 11
2[(3)(1)]<11
2+3<11
5<11YES
x=1
23x < 11
2[(3)(1)]<11
23<11
1<11YES
Let's verify by pluggingin a few points outside of this domain...
x=4
23x < 11
2[(3)(4)]<11
2+12<11
13<11NO
x=5
23x < 11
2[(3)(5)]<11
215<11
13<11
13<11NO
3/2/2014

Vivian L.