Question

solve the inequality, show work
-6-(t+8)<2(11-3t)+4

Answer 1

First you need to get rid of the parenthesis. You need to distribute the numbers through the parenthesis. Do you know how to do that ?

Answer 2

@texaschic101 nope

Answer 3

Ok....look at the numbers right before the parenthesis....and if it is just a sign (negative or positive, the number is 1. The first parenthesis, the number before it is -1. Multiply everything in the parenthesis by a -1. In the second parenthesis, the number before the parenthesis is 2 so multiply everything in the parenthesis by 2.
-6 - (t + 8) < 2(11 + 3t) + 4
-6 - t - 8 < 22 + 6t + 4
Do you understand how I got that ?

Answer 4

@texaschic101 yes, I do understand where you got that from, and what do i do from there?

Answer 5

combine like terms on each side...
-6 - t - 8 < 22 + 6t + 4
- 14 - t < 26 + 6t
you see how I got that ?

Answer 6

@texaschic101 yes, now what's next?

Answer 7

you want to get the t's on one side and everything else on the other side. So first you want to subtract 6t from both sides...
- 14 - t < 26 + 6t
- 14 - t - 6t < 26 + 6t - 6t
- 14 - 7t < 26

and then you want to add 14 to both sides to get - 7t by itself.
- 14 - 7t < 26
- 14 + 14 - 7t < 26 + 14
- 7t < 40

Do you understand what I just did ?

Answer 8

yes I do, then do i divide 7 to the -7t<40? @texaschic101

Answer 9

you then divide by a -7, but remember in inequalities, dividing by a negative number changes the sign. So, what answer did you get ?

Answer 10

@texaschic101 um is the answer going to be 5.7

Answer 11

- 7t < 40
-7t/-7 > 40/-7 (negative divided by a positive is a negative)
t > - 5 5/7
t > - 5.7 <---t is greater then - 5.7) remember we had to flip the sign since we divided by a negative number.

Answer 12

@texaschic101 I understand now, so how do i write that in set notation and interval notation?

Answer 13

that I dont know...sorry....you might need someone else to help you with that.
Look at this and see if it helps...
http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html

Answer 14

@texaschic101 thanks! and is the answer for 6y+5>-13 = y>1.3

Answer 15

No, you messed up somewhere...
6y + 5 > -13
6y + 5 - 5 > -13 - 5 (subtract 5 from both sides to get 6y by itself)
6y > - 18
6y/6 > -18/6 (divide by 6 to get y by itself)
y > - 3

Answer 16

Did you find your mistake ?

Answer 17

I see what you did...you didn't get a - 18, you got an 8. When adding two negatives together, the outcome is a negative. And - 13 + (-5) = - 13 - 5 which equals - 18.

Answer 18

@texaschic101 yes i understand, thanks for your help ( :

Answer 19

you are very welcome....thats what I am here for :)