Question 6886: I am having trouble with Inequalities, Permutations, and Probability. I was not sure what this question fit into, I hope that is alright. I am having trouble solving the inequality, -4y + 6<-14? I got it wrong on my homework, I had the answer y>2, Can someone please tell me what I did wrong?
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! I can't say what you did wrong, but inequalities are similar to equalities in that you can add, subtract, multiply, and divide both sides and still have the same inequality. That is, if a < b and you add 2 to both, a+2 < b+2, etc.
The one thing you can't do is change the sign.
Think of it this way: 2 is less than 3, but -2 is greater than -3.
To show this with inequalities you would write
2 < 3
-2 > -3 [multiplying by -1, which changes the sign]
In your case you can solve
-4y + 6<-14
-4y < -14 - 6 [subtracting 6 from both sides]
-4y < -20
This also means
4y > 20 [multiplying by -1 and changing the relational operator]
y > 5 [dividing both side by 4]
Checking: when y=5, the inequality is not true (-4x5 + 6 = -14 which is NOT LESS than -14).
When y is anything less than 5, the inequality -4y + 6 gets larger than -14 because -4y gets larger.
But when y is anything greater than 5, the inequality gets smaller than -14 because -4y gets smaller.
Perhaps you have a problem with -30 being smaller than -4? Remember, "smaller" means further to the left on the real number line.
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