SOLUTION: I am stuck on this problem. Solve the compound inequality 6>-4x+5 or 12≤-3x+5? I come up with x> -1/4 and x≤-7/3, but the multiple choice answers do not match. ANS

Algebra ->  Finance -> SOLUTION: I am stuck on this problem. Solve the compound inequality 6>-4x+5 or 12≤-3x+5? I come up with x> -1/4 and x≤-7/3, but the multiple choice answers do not match. ANS      Log On


   

Question 512390: I am stuck on this problem.
Solve the compound inequality 6>-4x+5 or 12≤-3x+5?
I come up with x> -1/4 and x≤-7/3, but the multiple choice answers do not match.
ANSWERS
A. (-∞, 7/3]
B. (-1/4, ∞)
C. (-∞,∞)
D. (-∞,-7/3] U (-1/4, ∞)
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the compound inequality 6>-4x+5 or 12≤-3x+5?
I come up with x> -1/4 and x≤-7/3, but the multiple choice answers do not match.
6 > -4x + 5
12<= -3x+5
---------------------
Solve the 1st for "x":
4x+6 > 5
4x > -1
x > -1/4
----------------
Solve the 2nd for "x":
3x+12 <= 5
3x <= -7
x <= -7/3
----
Solution -1/4 < x OR x <= -7/3
================================
Answer: D
===============
Cheers,
Stan H.
===========
ANSWERS
A. (-∞, 7/3]
B. (-1/4, ∞)
C. (-∞,∞)
D. (-∞,-7/3] U (-1/4, ∞)

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Yes it does match D) but the word between them is OR, not AND

 6 > -4x+5 OR 12 ≤ -3x+5

4x > -1   OR  3x ≤ -7

 x > -1%2F4   OR x ≤ -7%2F3

That's the same as 

 x ≤ -7%2F3 OR  x > -1%2F4   

 x ≤ -2%261%2F3 OR  x > -1%2F4

The graph of that is

<====================⚫------------------⚪================================> 
-4          -3          -2          -1           0           1           2  

The circle on the left is closed because the inequality is ≤ and the one on 
the right is open because it's >.

and the interval notation for that is

  (-∞,-7/3] ∪ (-1/4, ∞)

The interval notation is just an abbreviation for the graph on the 
number line above:

The ] indicates that -7%2F3 IS included in the solution set,
The ( indicates that -2%261%2F3 is NOT included in the solution set,
the ∪ indicates "OR", indicating a "jump" in the shading. 

Edwin