Question 1755: I need how to solve and verify the solutions:
1. r+7>-5
2. -35 +6n<7n
3. -14+p>4-(-2p)
4. x-5>-3/3
5. 4(n-1)<7n+8
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! to answer you, I will have to assume that you understand straight line graphs and you can sketch them from "y=mx+c"...I am English, and i assume you are American so i hope you know what i mean by y=mx + c. If not, we are stuck.
Anyway..inequalities are very easy...no sweat. Treat them just like normal equations. The ONLY difference is when you have to multiply or divide by a negative number...THEN the inequality sign changes round.
so, number 1:
let us do 2 equations. First r+7=-5
1. move the 7 to the other side, gives r = -12. Done!
Now, lets do, r+7>-5
1. move the 7 to the other side, gives r > -12. Done!
Easy :-)
OK, second equation is -35+6n < 7n
First, move the 6n to the other side (by subtracting 6n). So, we then have -35 < n. The n (or more formally 1n) came from 7n - 6n
So this is the answer....n > -35...all i have done is write the whole of "-35 < n" the other way round...no maths.
I shall leave you with 3 and 4.
As for verifying...draw a graph of y=-12 (or r=-12, whatever). This line is where y (or r) EQUALS -12. You want everywhere where y (or r) is GREATER than -12... so shade everywhere where that is true.
Similarly, for number 2, draw the graph (straight line) of n=-35. Then shade the region of the graph where n is GREATER than -35...
Hope this helps
Jon
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