Question

Solve the inequality and graph its solution: –7 < 2s + 5 < 15

Answer 1

@whpalmer4 Can you help me here?

Answer 2

this is a one-dimensional inequality, right? the whole thing fits on a number line

Answer 3

Yes

Answer 4

so let's draw the number line, with the part we know...

as in, you draw it :-)

Answer 5

well, okay, I guess we have to do a bit of work first.

Answer 6

\[-7<2s+5<15\]are we going to use open circles or closed circles to draw our solution?

Answer 7

I have answer choices but there all images

Answer 8

no sweat, we can do without them, we're going to find the answer, not just rule out the wrong ones :-)

Answer 9

And i think its closed. Im reviewing for my an exam and its things i learned awhile ago and i kinda forgot. So bare with me

Answer 10

"bear with me" :-)

we want open circles, because we have < or >
closed circles include the endpoint, open circles do not

Answer 11

*takes note* So we use closed circles got it

Answer 12

no, we need open circles!

Answer 13

if we had \[-7 \le 2s+5\le 15\]we would use closed circles, because there the endpoint is included.

Answer 14

Lol no i meant we dont use them lol srry

Answer 15

okay. so now we break this into two problems:

\[-7 = 2s+5\]
\[15 = 2s+5\]If we can solve those, we know where the endpoints of the region are.

Answer 16

1) S=-19

Answer 17

Hmm, you sure about that?

Answer 18

lol no

Answer 19

its -6

Answer 20

that's better! how about the other one?

Answer 21

2) S=5

Answer 22

right. so the solution to our inequality has endpoints -6 and 5. we've established that the endpoints are not included. so now the only question is whether the region between -6 and 5 is the solution, or the region to the left of -6 and the region to the right of 5 is the solution.

Answer 23

I like to try these things out with 0. 0 makes most expressions very easy to compute :-)

Answer 24

Sweet that is now bringing back my memory. Thanks i get it now. Your awesome!

Answer 25

so, if 0 satisfies the inequality, then the region containing 0 is what we shade.

\[-7 < 2s + 5 < 15\]\[-7 < 2(0) + 5 < 15\]\[-7 < 5 < 15\]That's true, so we shade the area between -6 and 5. I think you should have an answer that looks like that, right?