SOLUTION: Good evening. I am taking a college level business calculus class. We are currently reviewing algebra. I am stuck on one problem. It is: A-5 ----

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Question 341756: Good evening. I am taking a college level business calculus class. We are currently reviewing algebra. I am stuck on one problem. It is:
A-5
---- < -1
A+2

I know to take the -1 times A + 2 to get A - 5 < A + 2 and I know to take the +2 and subtract it from A - 5 to get A - 5 - 2, but what happens to the A on the right side. Is it not supposed to be a 0? I am really confused and lost and, therefore, unable to continue because the rest of this section contains similar problems. Please help me figure this problem out.

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A-5
---- < -1
A+2
---------------------
The boundary of the inequality is (A-5)/(A+2) = -1
-------------------
Since the denominator cannot be zero, A cannot be -2.
---
The numerator cannot be zero so A cannot be 5
-------------------------------
To solve the inequality:
1: Draw a number line
2: Plot the values A = -2 and A = 5
3: Check a test value from each of the resulting 3 intervals
to see where the solutions are for the inequality.
----
A-5
---- < -1
A+2
Check A = -10; (-10-5)/(-10+2) < -1, false so no solutions in (-inf,-2)
Check A = 0; (0-5)/(0+2)< -1, true so solutions in (-2,5)
Check A = 10; (10-5)/(10+2) < -1, false so no solutions in (5,+inf)
====
Final solution: -2< A < 5
============
Graph:

============
Cheers,
Stan H.

Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!

The other tutor's solution is incorrect. It should be

Good evening. I am taking a college level business calculus class. We are currently reviewing algebra. I am stuck on one problem. It is:
A-5
---- < -1
A+2

I know to take the -1 times A + 2 to get A - 5 < A + 2

There's one of your errors! -1 times A + 2 is -1(A + 2) and then you use the distributive principle to remove the parentheses, and you end up with -A - 2, (not A + 2). But also when you multiply through by a variable quantity, A + 2, if that quantity happens to be negative you would have to change the direction of the inequality. So would only become if which is the same as But it would become if which is the same as So two cases must be considered to which if either is valid of if they both are: Solving the first case Case 1: if or Add A to both sides: if if Add 5 to both sides if if Divide both side by 2 if That gives us the solution set: -------------------- Solving Case 2: if or Add A to both sides: if if Add 5 to both sides if if Divide both side by 2 if This is a contradiction, since A cannot be greater than and at the same time be less than or equal to -2, so the only solution is given by case 1. Edwin

SOLUTION: Good evening. I am taking a college level business calculus class. We are currently reviewing algebra. I am stuck on one problem. It is: A-5 ---- < -1 A+2 I know t