Question

Given: A = {18,6,-3,12}
Determine all elements of A that are in the solution of the inequality 2/3x +3<-2x-7

Answer 1

i need an answer!!!

Answer 2

Have you tried inputting each number into x one at a time and evaluating the inequality?

Answer 3

oh wait, it is
\[\frac{2}{3}x +3<-2x-7\]

Answer 4

i have an idea. before plugging in the numbers, lets solve this for x. then it will be easy

Answer 5

okay.

Answer 6

multiply both sides by 3 to get rid of the annoying fraction. be careful to multiply everything by 3

Answer 7

\[2x+9<-6x-21\]

Answer 8

okay

Answer 9

fraction is gone ok?

Answer 10

k

Answer 11

add 6x to both sides to get
\[2x+6x+9<-21\]
\[8x<-21\]

Answer 12

subtract 9 from both sides to get
\[8x<-21-9\]
\[8x<-30\]

Answer 13

okay

Answer 14

and now divide by 8 to get
\[x<-\frac{30}{8}\]
\[x<-3.75\]

Answer 15

now just look at your list of numbers. if it is less than -3.75 say
"yes" and if it is not say "no"
done!

Answer 16

omg! . .that was easier! thank you

Answer 17

in fact i do not see any that are, do you?

Answer 18

Hold on!

Answer 19

the answer is -12

Answer 20

i may have made a mistake, let me check

Answer 21

no, no mistake it is right!

Answer 22

one of the above anwers shouldve been -12 . i accidentally put 12

Answer 23

i don't see -12 in your list. oh ok

Answer 24

you were right the first time plugging it in. i wasn't so sure about solving for x

Answer 25

ok that is the answer. a lot easier to solve first, plug in the number last

Answer 26

is it clear how to solve? like solving for x pretty much. just make sure if you have to divide by a negative number to change the inequality

Answer 27

hold on..ima plug it into a calculator so i can check it

Answer 28

im confused lol