Question

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

Answer 1

solve the inequality first
and determine which numbers are in that solution set in the set A

Answer 2

or you can plug each of the elements of A into the inequality and see if the inequality holds
if it holds, then that element is a solution of the inequality

Answer 3

alrightt

Answer 4

for example lets look at x=18:
2(18)/3+3<-2(18)-7
12+3<-36-7
15<-43 this statement is false therefore 18 is not in the solution set

Answer 5

ooooooooo ok

Answer 6

x=6:
2(6)/3+3<-2(6)-7
4+3<-12-7
7<-19 is also false so 6 is not in the soluton set
x=-3
2(-3)/3+3<-2(-3)-7
-2+3<6-7
1<-1 false so -3 is not a solution
x=-12
2(-12)/3+3<-2(-12)-7
-8+3<24-7
-5<17 is true so x=-12 is in the solution set

Answer 7

the other way solve for x in the above expression we have
2x/3+3<-2x-7
get your x together and everything w/o an x on opposing side
2x/3+2x<-7-3
2x/3+6x/3<-10
8x/3<-10
x<-10(3/8)
x<-30/8
x<-15/4

Answer 8

which of the numbers above are less than -15/4?

Answer 9

in set A, which elements are less than -15/4?