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

can you solve the inequality?

Answer 2

idk how to im blanking out right now hah

Answer 3

could you solve this inequality: 3x <2x +1?

Answer 4

subtract 2x fom both sides

Answer 5

x<1

Answer 6

yep, so do same thing here
2/3x +3 <-2x - 7

make that all x's would be in left hand side, how you can do that?

Answer 7

add -2x so 4/3 x?

Answer 8

2/3 is fractional ~ 1.333 so adding 2 would be ~3.333 or better \[\frac{2}{3}+2=\frac{2}{3}+\frac{6}{3}=\frac{8}{3}\]

Answer 9

so what you have left now when you added 2x?

Answer 10

8/3x+3<-7 then add 3 and you get 8/3<-4?

Answer 11

if you add 3 to both sides you get
8/3x+3+3<-7+3
8/3x+6<-4
is it correct?

Answer 12

so it would be 8/3x<-10?

Answer 13

yes and one more step left, what it is?

Answer 14

plug in the numbers for x?

Answer 15

no, if you had 2x<6, how would you solve it?

Answer 16

divide by 2 on both sides

Answer 17

so you have to divide there as well by that fraction

Answer 18

as a decimal its -0.26666666666

Answer 19

you dont know how to divide fractions? you have to invert second one to change it to the multiplication
\[\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}=\frac{a\times d}{b\times c}\]

Answer 20

oh yeah sorry im blanking out so much right now

Answer 21

i got x<-30/8

Answer 22

yeah, now just convert to decimal for easier comparison and select numbers from A

Answer 23

okay thank you so much!!!!!!!!!!!!!!!!! you helped so much thank you

Answer 24

your welcome :)