SOLUTION: Hello, I am having trouble with inequalities. I have to label each statement as true or false. If 3<x, then 3+y<x+y. I think this is true, because when I solved for x, x>3. If

Algebra ->  Inequalities -> SOLUTION: Hello, I am having trouble with inequalities. I have to label each statement as true or false. If 3<x, then 3+y<x+y. I think this is true, because when I solved for x, x>3. If       Log On


   

Question 1005351: Hello, I am having trouble with inequalities. I have to label each statement as true or false. If 33. If -4<-2t+6<10, then 2>t+6>-5. I am not sure how to figure this one out. I appreciate your help!
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+-4+%3C+-2t+%2B+6+%3C+10+
You can split this up into 2 statements:
(1) +-4+%3C+-2t+%2B+6+
(2) +-2t+%2B+6+%3C+10+
-------------------
Subtract +6+ from both sides of (1)
(1) +-10+%3C+-2t+
This is tricky. I want to divide both sides by +-2+
The rule says that whenever you divide an inequality
by a negative number, you then must reverse the
inequality sign, so I'll do that
(1) +5+%3E+t+
or, what is the same thing:
(1) +t+%3C+5+
--------------
(2) +-2t+%2B+6+%3C+10+
Subtract +6+ from both sides
(2) +-2t+%3C+4+
Follow the same rule again for dividing by a negative number
(2) +t+%3E+-2+
--------------
This says the value of +t+ lies between +-2+ and +5+
-----------------------------------
Now do the same thing with the other inequality
+2+%3E+t+%2B+6+%3E+-5+
(1) +2+%3E+t+%2B+6+
(2) +t+%2B+6+%3E+-5+
------------------
subtract +6+ from both sides of (1)
(1) +-4+%3E+t+
(1) +t+%3C+-4+
--------------
subtract 6 from both sides of (2)
(2) +t+%3E+-11+
----------------
What (1) and (2) say is that the value of +t+
is between +-11+ and +-4+, and this
would violate the other inequality.
I would choose false.
------------------
It's easy to make mistakes with these. It helps
to draw where they are on the number line and
you can see what's happening. Know the rules
and follow them. Hope this helps

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The basic strategy for inequalities and equations is the same.
here are theorems you need to remember:
Theorem 1.
We may add the same number to both sides of an inequality, and the sense will not change.
If a+%3E+b, then a+%2B+c+%3Eb+%2B+c.
Theorem 2.

We may multiply both sides of an inequality by the same positive number, and the sense will not change.
If a+%3E++b, and c+%3E+0, then ca++%3E+cb.
Theorem 3.
If we multiply both sides of an inequality by the same negative number, the sense of the inequality changes.
If a+%3E++b, and c+%3C+0, then ca++%3C+cb.


If 3+%3C+x, then 3%2By%3Cx%2By=>TRUE


If -4%3C-2t%2B6%3C10, then 2%3Et%2B6%3E-5=>NOT TRUE
-4%3C-2t%2B6%3C10....both sides divide by -2
-4%2F-2%3C-2t%2F-2%2B6%2F-2%3C10%2F-2
highlight%282%3Et-3%3E-5%29 and it is not equal to 2%3Et%2B6%3E-5