Compound Inequalities:What are the steps and answers for -5x<-25 and -2x>-12?

Question

P.S.the second sign is greater than or equal to...Thanks!

Answer 1

This is done exactly the same as a equality equation except when you multiply or divide by a negative the inequality sign is reversed.

-5x <-25 (divide both sides by -5 and reverse the inequality sign)
x>5

-2x>-12 (divide both sides by -2 and reverse the inequality sign)
x<6 (or equal to)

you can check either answer by pluging a value that satisfies the answer into the original equation.

ie. for the second equation x < 6 so if we let x = 5 then
-2(5)>-12 should be true
-10>-12 is true.

Answer 2

This is saying that -5x is less than -25. So that means x is a number when combined with -5 is less than -25. -5(5.1)=-25.5 and it is a number less than -5 so this is correct. And the other part is saying -2x is greater than or equal to -12. So -2 multiplied with a number so that it is equal to or greater than -12 would be the answer. See look this is correct -5(6)<-25 and -2(6)>=-12

I used the plug in method which is fairly easy.

Answer 3

a) well for -5x<-25 I would do this:
-divide both sides by 5 and since 5 is negative, you would change the sign so it would be like this: x>-25/-5
So the answer would be:
x>5
b) for this one, -2x>(or equal to)-12
- same thing applies to this one. Divide both sides by 2 and since 2 is negative, you change the sign, so it should be:
x<(or equal to) -12/-2
So tha answer is:
x<(or equal to)6

Hope this helps:)

Answer 4

first you divide both sides by -5 and the sign will turn the other way so the answer be x>5 and on the other you divide both sides by -2 and the sign will turn and the answer is x<6 (or equal to) hope i helped

Answer 5

Solve for x.

-5x < -25 and -2x ≥ -12

Let's start with

-5x < -25

Add 5x + 25 to both sides.

25 < 5x
5 < x
____________

-2x ≥ -12

Add 2x + 12 to both sides.

12 ≥ 2x
6 ≥ x
x ≤ 6
_____________

So we have:

(5 < x) and (x ≤ 6)

Both conditions are satisfied for

5 < x ≤ 6

Answer 6

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Answer 7

the first one will be -5x/-5<-25/-5 which = x>5
the second will be x<=6

Answer 8

well you divide by negative 5 for both sides so it would be x>5
..etc...