Is the inequality always, sometimes or never true? 9(x+2) 9(x-3) answer is 23 and i said it's never true, right? 2. 6x-13

Question

Is the inequality always, sometimes or never true? 9(x+2) > 9(x-3) answer is 2>3 and i said it's never true, right? 2. 6x-13 < 6(x-2) answer is 6x-13 < 6x-12 my answer is sometimes 3. -6(2x-10) + 12x less than or equal to 180. im stuck.

wolfe8 · Answer

If you did the first and second inequality correctly then you are right. A way to check for number 2 is by putting in a negative number, zero, and positive number for x and see what happens. 

So basically for number 3 you have $$-6(2x-10)+12x \le180$$ Solve for x and see.

awkwardpanda · Answer

Oh okay so for number 2 it would be 13<2 which is never true and as for 3, it's 60. 

so it would be 60 less than or greater than 180.. which is always true.

awkwardpanda · Answer

Right? Idk.

awkwardpanda · Answer

I have a strong feeling the first one is never true. the second one is never true and the third one is always true.

wolfe8 · Answer

Well the first one is $$9x+18>9x-27$$So it is saying a number plus 18 is more than the same number minus 27. Do you think that is true?

Second one $$6x-13<6x-12$$ is saying that a number minus 13 is smaller that the number minus 12. What do you think? 

Third one$$-6(2x-10)_12x \le180$$$$-12x+60+12x \le180$$$$60\le180$$What do you think?

awkwardpanda · Answer

1. Sometimes true. 
2. true.
3. true. 
:3 .-.

wolfe8 · Answer

Is that the right answer you checked? As I said, use negative,positive and zero numbers as x to check. Use 1,-1 and 0 for simplicity. When I replaces x in number 1 with 1, I get 27>-26. When I use -1 I get 9>-36. When 0, 18>-27 Are those all true?

awkwardpanda · Answer

So 1. Would be true, yes. 2. True and 3rd is true. Unless I keep doing the math wrong.

wolfe8 · Answer

Well....3 ends up saying 60 is less than or equal to 180. I think that's always true unless it's considered sometimes true for some reason. Do you have the answer for this so I can check?

awkwardpanda · Answer

SO 1. is 18 > -27 , right? and 2 is 13 < 12, right?

wolfe8 · Answer

Any positive number is always larger than a negative number. And you might want to check for number 2 again. I did not get 13<12. You might want to watch out for signs. :)

awkwardpanda · Answer

wait wait. it's both negative. -13<-12 right?

wolfe8 · Answer

Yup.

awkwardpanda · Answer

OH!!! Hahaha. So it's true!

wolfe8 · Answer

Yup :) Good job

awkwardpanda · Answer

YAY! 30 problems finished THANK YOU SO SO MUCH.

wolfe8 · Answer

You're very welcome.