1>2h+3>-1
1>2h+3
2h>2
h>1
2h+3>-1
2h>-4
h>-2
Is this right?
no, it's wrong
if
1>2h+3
-2>2h
Is h>-1?
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
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
Yes, your reasoning is correct! Let's break down the steps to solve the inequality 1 > 2h + 3 > -1:
1) Start by solving the left-hand side inequality: 1 > 2h + 3
Subtract 3 from both sides to isolate 2h: 1 - 3 > 2h
Simplify: -2 > 2h
Divide both sides by 2: -1 > h
Flip the inequality sign to maintain the same direction: h < -1
2) Now let's solve the right-hand side inequality: 2h + 3 > -1
Subtract 3 from both sides: 2h + 3 - 3 > -1 - 3
Simplify: 2h > -4
Divide both sides by 2: h > -2
Combining the results from both inequalities, we have h < -1 and h > -2. So, the solution for h is -2 < h < -1.