Question

1>2h+3>-1

1>2h+3
2h>2
h>1

2h+3>-1
2h>-4
h>-2

Is this right?

Answer 1

no, it's wrong
if
1>2h+3
-2>2h

Answer 2

Is h>-1?

Answer 3

I am going to do this very slowly

1>2h+3>-1

now subtract 3 from everything

-2 > 2h > -4

now divide everything by +2 (by the way if you divide or multiply by a NEGATIVE number, you change the directions of arrows - keep that in mind although we do not need it here).

-1 > h > -2

I personally would write that as

-2 < h < -1

because I like to think from left to right on a number line

Answer 4

NOW
Go back and check the answer.
Here is your problem statement:

1>2h+3>-1

and I said the solution was:

-2 < h < -1

So try h = -2
then
1 > 2*-2 +3 > -1 ????
1 > -4+3 > -1 ???
1 > -1 >-1 yes, as expected right on the border
Now try h =-1 ,that should be on the other border
1 > 2*-1 +3 > -1 ???
1 > -2 + 3 > -1 ???
1 > 1 > -1 yes, sure enough
Now try a number between h = -1 and h = -2
For example h = -1.5
then
1 > 2*-1.5 +3 > -1 ???
1 > -3 +3 > -1 ???
1 > 0 > -1 sure enough, 0 is grater than -1 and less than +1