Question

What is the solution of 5a + 12 < 2 and 5a - 12 < 3?
A. a < -2
B. a < -1.8
C. a < 2.8
D. a < 3

Answer 1

@InYourHead

Answer 2

Help me hermano!!!

Answer 3

I don't know how to do this.

Answer 4

I don't either. Hold on.

Answer 5

Okay. I think I've got it.

Answer 6

You sure you don't wanna ask someone else?

Because I'll tell you the truth: Math really isn't my field. I'm not at all confident in this section as other people are.

Answer 7

I'll tell you how I did it.

You can ask someone else just to be sure, if you like.

Answer 8

ok

Answer 9

@CliffSedge

Answer 10

There are two equations here.

5a + 12 < 2

And.....

5a - 12 < 3

-------------

I changed the < signs into = signs.

So....

5a + 12 = 2

And.....

5a - 12 = 3

Answer 11

Now, we need to get all of the number onto the LEFT side of the equal sign.

So......here are the two new equations, after we do that.....

5a + 12 - 2 = 0

And.....

5a - 12 - 3 = 0

Answer 12

There's an easier way..

Answer 13

a=-5
a=3

Answer 14

We can simplify those equations. You know...make them simpler.

So we have this.....

5a +10 = 0

And....

5a -15 = 0

Answer 15

NO.

Answer 16

I mean...no. Not quite.

Answer 17

Let's look at the first new, simplified equation....

5a + 10 = 0

Answer 18

In this case, a = -2

Answer 19

See?

Answer 20

ohh right
im doing things in my head

Answer 21

Now,
let's look at the second simplified equation.

5a - 15 = 0

In THIS case....a = -3

Answer 22

I mean 3.

Answer 23

Sorry. In this case....a = 3

Answer 24

So these are the two numbers we have, for a.....

a = -2
a = 3

Answer 25

Right.

Answer 26

Now,
let's change the = signs BACK into their original forms.

We change them back into < signs.

Answer 27

a < -2
a < 3

Answer 28

Now, which one is more specific, in this case?

We know that ( a ) has to be < 3.

Answer 29

But we know that ( a ) ALSO has to be < -2

Answer 30

Ok.

Answer 31

So you see.....a < -2 is a more SPECIFIC rule.

Answer 32

Is that tricky to imagine?

Answer 33

kinda yes.

Answer 34

Okay.

Well, let's look at the first rule that we discovered.

a < 3.

If this is the only rule,
then ( a ) could be anything less than 3.

( a ) could be 2, or 1, or 0....right?

Answer 35

ohh yes!

Answer 36

BUT NOW....look at the OTHER rule....

a < -2

Answer 37

We have TWO rules, not just one.

a < 3....AND....a < -2

Answer 38

( a ) can only be a number that fits BOTH rules.

Answer 39

Could ( a ) be 1 ??

Answer 40

yes

Answer 41

No, it can't.

Because 1 IS less than 3.

But 1 is NOT less than -2

Answer 42

a < 3

AND

a < -2

Answer 43

wait soory a can be anything -3 -4 -5

Answer 44

Right.

Answer 45

and soo on

Answer 46

Right.

So, the answer that I got for this problem was choice A.

a < -2

Answer 47

Because if (a < -2) .....
then it would fit both rules.

Answer 48

Anything less than -2 would make it so that ( a ) fits both rules.

Answer 49

Thanks man.

Answer 50

Yeah. That's my opinion. Get someone else's opinion if you like. I'd recommend it.

Sorry, math isn't my best area.