Solving Compound Inequalities?

Question

How do I write x+1>-2 and x+1<6
without using and? Could you please explain it? I don't get how to write it without and.

how do you slove
-2

Answer 1

rewrite the inequalities so they express the relations in terms of x by itself:
x + 1 > -2  ⇒  x > -3
x + 1 < 6  ⇒  x < 5

Now get the inequalities pointed in the same direction:
x > -3  ⇒  -3 < x
 x < 5  no change needed

and combine them:
-3 < x and x < 5 
∴ -3 < x < 5 

This could also be written in decreasing order (5 > x > -3), but the convention is to use increasing order  (-3 < x < 5) because that's the way the number line is oriented.

Answer 2

x+1 > -2 so -2 < x+1 and x+1 < 6.
Then : -2 < x+1 < 6

Answer 3

First, get the x's by themselves in each. Subtracting 1 from both sides of the first, you have x>-3. The other you'll have x<5. So, then, organize this so all your inequalities face the same way. You have -35, because if you wrote it 5

Answer 4

u write it like this 6>x+1>-2

all you do is put the common side of each equation and according to the facts you fill it in. I put x+1 in the middle and 6 on one side while 2 is on the other. This way it is one equation and both facts are true

Answer 5

Lol I just did this in math a week or so ago i really can't remember.. errrrrrr

I'll look wait lol.

x > -1 -2
x> -3

x> -1 +6
x>5

Collect the x's on one side, and then the numbers on the other

Always collect the x's where there are most x's to start with

so if it was

2x < x + 1

Put the x on the 2x side

2x-x<1
x<1

Answer 6

-2 < x+1 (put the lowest number 1st)
and
x+1 < 6 (put the highest number last)
-2 < x+1 < 6 (which puts the x-expression in the middle)