Question

Choose the correct description of the graph of the compound inequality

x - 2 > -3 and 3x 12

A number line with an open circle on -1, shading to the left, and a closed circle on 4, shading to the right.

A number line with an open circle on -1, a closed circle on 4, and shading in between.

A number line with a closed circle on -1, shading to the left, and an open circle on 4, shading to the right.

A number line with a closed circle on -1, an open circle on 4, and shading in between.

Answer 1

\(x - 2 > -3 \color{red}{\text{ OK}}\)
and \(3x\;\; 12 \color{red}{\text{ HUH?}}\)

Answer 2

less than or equal to

Answer 3

<=

Answer 4

OK. So, start by getting x alone. Know how to do that?

Answer 5

- the -3 from -3 and 12?

Answer 6

Well, for the first one, if you add 2 to both sides, what happens?

Answer 7

add 2 to 2 and -3

Answer 8

Yes. So what does the equation become?

Answer 9

x>-5

Answer 10

Take a second try at that: \(x - 2+2 > -3 +2\) You did the left side just fine... but the right.

Answer 11

or im sorry is it x>-1

Answer 12

Perfect!

Answer 13

So, your x must be greater than -1. That is part of the answer. Now, do you know how to mark the > on a number line, how that would be drawn? vs >=

Answer 14

well the -1 would be open circle to the right and the less than or equal to will be closed circle

Answer 15

Yes. OK, so, you just eliminated two possible answers! It will be open on -1.

Answer 16

B

Answer 17

So now you need to solve \(3x\le 12\) for x.

Answer 18

Yep. That is it!

Answer 19

Yes! Thanks!
can you possibly help with another?

Answer 20

Sure.

Answer 21

Determine the type of boundary line and shading for the graph of the inequality -3x + y > 6.

Answer 22

Dashed line with shading on the side that includes the origin.

Solid line with shading on the side that does not include the origin.

Dashed line with shading on the side that does not include the origin.

Solid line with shading on the side that includes the origin.

Answer 23

Usually, you want to get these where the y is on one side, the rest on the other. Then look for intercepts like it was a line. Once you know the intercepts, you can make the border line and have an idea what it would be.

Answer 24

y>3 is that the answer ?

Answer 25

No. How would you move the -3x over to the other side?

Answer 26

im not really sure i really dont know how to do this one

Answer 27

Well, have you done things like -3x+y=6 with the instruction of "Solve for y" ?

Answer 28

I have to go thank you for your help and time! goodbye

Answer 29

Bye.