2x - 3 < x + 2 ≤ 3x + 5
Let's break this up into two parts.....
First.......
2x - 3 < x + 2 (add 3 to both sides)
2x < x + 5 (subtract x from both sides)
x < 5
Secondly.......
x + 2 <= 3x + 5 (subtract 5 from both sides)
x - 3 <= 3x (subtract x from both sides)
-3 <= 2x (divide both sides by 2)
-(3/2) <= x (which also means x >= -(3/2))
Thus.........-(3/2) <= x < 5
Or in interval notation...... [-(3/2), 5)
Try picking some values "outside" this interval. You'll find that they won't satisfy both inequalities!!
Good luck!! Hope this helps.
