3x-2>2x-5
subtract 2x from both sides
x-2>-5
add 2 to both sides
x>-3
---------------------
2+x>2x+3
subtract x from both sides
2>x+3
subtract 3 from both sides
-1>x
swap sides but remember that if you swap sides you have to turn the inequality around
x<-1
--------------------------------
Now if you want the union of these. That is where either one or the other is true that would be all real x
If you want the intersection of these. Where they are both true then the answer is -3 < x < -1
3x-2>2x-5
subtract 2x from both sides
x-2>-5
add 2 to both sides
x>-3
---------------------
2+x>2x+3
subtract x from both sides
2>x+3
subtract 3 from both sides
-1>x
swap sides but remember that if you swap sides you have to turn the inequality around
x<-1
--------------------------------
Now if you want the union of these. That is where either one or the other is true that would be all real x
If you want the intersection of these. Where they are both true then the answer is -3 < x < -1