Question

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Answer 1

Any ideas?

Answer 2

Why don't we start by simplifying the first two answers and converting the last two into expressions?

Answer 3

5x > 35 or 5x < -35

Can you solve these for 'x'?

Answer 4

Yes, you get those, but you need to keep it in the same form.

x > 7
x < -7

Answer 5

Is -6 a solution to this?

Answer 6

Yep, so move on to the next one.

Answer 7

-8 < x - 5 < 3

Can you simplify this?

Answer 8

Yep! You want to isolate 'x' so you have to add 5 to all sides.

Answer 9

Now is -6 a solution to this one?

Answer 10

That's correct, so move on to the next one, can you change that into expression form like the first two options?

Answer 11

"Two less than a number tripled"

Can you change that

Answer 12

Yep, now do the last part of it.

"at least -5 and at most 1"

Answer 13

Do 'at least' first...what inequality symbol is that?

Answer 14

Not exactly, try answering my question above.

Answer 15

No, if you say "I have at least $5", what does that mean?

Answer 16

Exactly, so 'at least' means \(\ge\)

Answer 17

-5≥1

Answer 18

So we know that \(\sf 3x-2\ge -5\).

Answer 19

No, these are in relation to '3x - 2'. Now what does 'at most' mean?

Answer 20

Yes...if you say "I have at most $5", that means I could have $5 or less, which is \(\le\).

Answer 21

So we also know that \(\sf 3x-2\le 1\)

Answer 22

Is -6 a solution to \(\sf 3x-2\le 1\) or \(\sf 3x-2\ge -5\) ?

Answer 23

Remember, it has to be true for both, just plug in '-6' for 'x' in each one.

Answer 24

Yep, so on to the last one.

Answer 25

"The sum of 3 times a number and 5"

What does that translate to?

Answer 26

Yep, you got it. What about "is between -16 and 11"?

Answer 27

Well, it says 'is between', so we know it can't be equal to either -16 or 11.

To be between -16 and 11, what must be true about the relationship to 11?

Does it have to be less than or greater than 11?

Answer 28

Yep, because -16 is less than 11.

What about -16?

Does it have to be less than or greater than -16?

Answer 29

You got it. Because 11 is greater than -16.

So we know that 3x + 5 < 11 and 3x + 5 > -16. We can write this as:

-16 < 3x + 5 < 11

Now plug in -6 for 'x' and see if it works.

Answer 30

Yes, when you plug in -6 you get:

-16 < -13 < 11

-13 is certainly greater than -16 and less than 11.

So D is our answer.

Answer 31

\(\huge\checkmark\)

Answer 32

No problem.