SOLUTION: I need help with INDIRECT PROOFS. Given: -4x + 2 <-10 Prove: x > 3 All I know is that you have to do the opposite which would be -4x + 2 is greater than or equal to -10. That is

Question 262405: I need help with INDIRECT PROOFS.
Given: -4x + 2 <-10
Prove: x > 3
All I know is that you have to do the opposite which would be -4x + 2 is greater than or equal to -10. That is as far as I have gotten and I do not know where to go from there.
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
What makes you think you switch the sign?
You switch the sign when you multiply or divide by a negative number because the negative number line is opposite order of the positive number line.
-4x+2<-10
-4x<-12
now we are going to divide by -4
x>3
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
The basic goal of indirect proofs is you assume the opposite of what you are trying to prove as true and try to get some kind of contradiction. Lets see where this takes us . . .
STATEMENT #1: x <= 3
REASON #1: indirect assumption
STATEMENT #2: -4X + 2 < -10
REASON #2: Given
STATEMENT #3: -4x + 2 - 2 < -10 - 2
REASON #3: subtraction property of equality
STATEMENT #4: -4x < -12
REASON #4:additive inverse property
STATEMENT #5: -4x* (-1/4) > -12 * (-1/4)
REASON #5:multiplication property of equality
STATEMENT #6: x > 3
REASON #6:multiplicative inverse property
Notice we have a contradiction between step #1 and step #6. Since we have a contradiction, our assumption of statement #1 was false and therefore,
x > 3.
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