Question

if x squared +5 is less than 6 and 2x squared+7

is greater than 8, what is one possible value of x?

Answer 1

tips?

Answer 2

plug?

Answer 3

5.25 is less than 6 and 7.125 is less than 8

Answer 4

I used x=1/2

Answer 5

or is there a simpler way?

Answer 6

ahh

Answer 7

I see

Answer 8

add both equations

Answer 9

then solve for x

Answer 10

x^2+5<6 and 2x^2+7>8
x^2<1 and 2x^2>1
x^2<1 and x^2>1/2
1/2<x^2<1

Answer 11

I got the square root of 2/3

Answer 12

as being one of the square roots

Answer 13

so the square root of 2/3 could equal x

Answer 14

any simpler ways, guys?

Answer 15

3x squared +12 is less than 14

Answer 16

when 1/2 < x^2 < 1, which is true, all you have to do is take the square root of all 3 expressions. Then sqrt(1/2) < x < 1 and just pick a value in that range, but not sqrt(1/2) or 1.

Answer 17

how did you guys come up with the range?

Answer 18

wait

Answer 19

from solving the two equations?

Answer 20

x squared=1/2,1?

Answer 21

You might want to get in the very good (and necessary) habit of calling them inequalities as "equations" means equal on both sides. But yes, solve the inequalities and x^2 has to fall in that open range. Open means you cannot select the endpoints.

Answer 22

k

Answer 23

last section for the day is word problems

Answer 24

see you guys in 10-15 minutes

Answer 25

peace

Answer 26

thx for medal