Question

Determine the type of boundary line and shading for the graph of the inequality -4x - y > -6

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 1

please help

Answer 2

so you have -4x - y > -6

Answer 3

Below is an attached graph.

So see this one you first need to isolate y.

-4x - y > -6
-y > 4x - 6
y < -4x + 6 (remember when dividing or multiplying across a greater-than or less-than sign you swap the direction.)

So then you graph this, like I did. And what do you believe the answer is?

Answer 4

A

Answer 5

@Dragondd320

Answer 6

Indeed

Answer 7

@Dragondd320 can I ask you another question

Answer 8

Sure, what is your question?

Answer 9

Which of the following is not an equivalent form of the compound inequality

x + 10 > 25 and x + 10 less than or greater to 32

25 < x + 10 less than or greater to 32

A number line with an open circle on 15, shading to the left, and a closed circle on 22, shading to the right.

15 < x and x less than or greater to 22

A number line with an open circle on 15, a closed circle on 22, and shading in between.

Answer 10

Hmm. Let me work it out.

Answer 11

ok thank you @Dragondd320

Answer 12

@Dragondd320 can you solve this one too.....

Determine the type of boundary line and shading for the graph of the inequality y < 2x + 6

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 13

Which of the following is not an equivalent form of the compound inequality

x + 10 > 25 and x + 10 less than or greater to 32

25 < x + 10 less than or greater to 32

A number line with an open circle on 15, shading to the left, and a closed circle on 22, shading to the right.

15 < x and x less than or greater to 22

A number line with an open circle on 15, a closed circle on 22, and shading in between.

For this one the answer is B.

Answer 14

Determine the type of boundary line and shading for the graph of the inequality y < 2x + 6

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.

@Dragondd320

Answer 15

Look at that.

And tell me what you believe the answer is.

Answer 16

is that dashed or solid? @Dragondd320

Answer 17

Look at your equation for that answer.

If it is < or > : then it is a dotted line

If it is ≤ or ≥ : then it is a solid line

Answer 18

ok so I think its A again?

Answer 19

how do you know when it includes the origin ?

Answer 20

Look at the graph. Is (0,0) in the shaded region?

Answer 21

yes

Answer 22

(0,0) is called the origin, for it is where the two axis originate ;D

Answer 23

ok so if (0,0) is shaded the origin is included?

Answer 24

@Dragondd320

Answer 25

Yes, that is correct

Answer 26

so the answer is A?

Answer 27

@Dragondd320

Answer 28

Choose the correct description of the graph of the compound inequality

x - 1 less than or greater to 9 or 2x greater than or equal to 24

A number line with an open circle on 10, shading to the left, and an open circle on 12, shading to the right.

A number line with an open circle on 10, an open circle on 12, and shading in between.

A number line with a closed circle on 10, a closed circle on 12, and shading in between.

A number line with a closed circle on 10, shading to the left, and a closed circle on 12, shading to the right.
@Dragondd320

Answer 29

D

Answer 30

Which of the following is not an equivalent form of the compound inequality

x + 6 < 9 or x + 6 greater than or equal to 15

x < 3 or x greater than or equal to 9

A number line with an open circle on 3, a closed circle on 9, and shading in between.

x greater than or equal to 9 or x < 3

A number line with an open circle on 3, shading to the left, and a closed circle on 9, shading to the right.


@Dragondd320

Answer 31

Take a look at the wording.

It says:
x+6 < 9 or x+6 ≥ 15

So first simplify both for x.

Answer 32

im confusef

Answer 33

Well here is the first of the two.

x+6<9
x<3

So what would you do to the second one?

Answer 34

irealy don't know

Answer 35

Take a look. It is:

\[x + 6≥ 15\]

What would you do to get x by itself?

Answer 36

subtract it from both sides

Answer 37

@Dragondd320

Answer 38

subtract what?

Answer 39

x

Answer 40

@Dragondd320

Answer 41

No, not x from both side. Try something else.

Answer 42

i don't knwo

Answer 43

subtract 6? @Dragondd320

Answer 44

Yes, you would subtract it from both sides. This gives you your simplified expression.