Question

simplify |a-4|+|a+3|, given that -2 11 years ago

Answer 1

|a-4| is another way to say -(a-4)
and |a+3| is -(a+3) can you distribute the negative

Answer 2

not sure what "simplify" means in this context

Answer 3

|a-4|=-(a-4) if a-4<0
|a-4|=a-4 if a-4>0
|a-4|=0 if a-4=0

|a+3|=-(a+3) if a+3<0
|a+3|=a+3 if a+3>0
|a+3|=0 if a+3=0


So |a-4| will not always be -(a-4)
And |a+3| will not always be -(a+3)

Answer 4

what @myininaya said
you can write it as a peicewise expression, but that is no simpler than what you have

Answer 5

it says as |a-4|+|a+3|, given that -2<a<3.

Answer 6

Try to use the post above to rewrite your expression.
Everything you need is right here on that myininaya post.

Answer 7

For example that first inequality says a<4 when |a-4|=-(a-4)
The second inequality says a>4 when |a-4|=a-4

which one do you think you will need for |a-4|?

Answer 8

Are any of the values in the interval [-2,3] greater than 4?

Answer 9

no.

Answer 10

So what will |a-4| equal in this case?

Answer 11

a-4

Answer 12

So you are still looking at values greater than 4 even though you said no values in [-2,3] were greater than 4?

Answer 13

I.
|a-4|=a-4 if a>4
II.
|a-4|=-(a-4) if a<4

The I. says when I have values greater than 4 I will use that |a-4|=a-4

The II. says when I have values less than 4 I will use |a-4|=-(a-4)

Answer 14

You said none of the values in (-2,3) were greater than 4.

Answer 15

But all of the values in (-2,3) are less than 4.

Answer 16

Yes

Answer 17

So |a-4|= what in this case?

Answer 18

You only have two choices.

Answer 19

And I have given them to you
choice I or choice II

Answer 20

II

Answer 21

ok so |a-4|=-(a-4) when a<4 which it is because all of the values in (-2,3) are less than 4


now what about the |a+3|
look at my earlier post and think for a few minutes

Answer 22

Again you only have two choices

Answer 23

You do have to consider the numbers from -2 to 3

Answer 24

so will it be like, |a+3|=a+3 when a>3

Answer 25

|a+3|=a+3 when a+3>0 which means a>-3
|a+3|=-(a+3) when a+3<0 which means a<-3

Are the numbers in the interval (-2,3) less than -3 or greater than -3?

Answer 26

I am bad :(

Answer 27

Yes the numbers in the interval is greater than -3

Answer 28

Just follow this definition always to rewrite |f(x)| as a piecewise function
|f(x)|=f(x) if f(x)>0
|f(x)|=-f(x) if f(x)<0
|f(x)|=0 if f(x)=0

You will have to solve the inequalities/equalities
-----------------------------

and so that is why you chose |a+3|=a+3 because we had the the numbers in the interval (-2,3) is greater than -3
we have a is greater than -3

so
you have:
simplify |a-4|+|a+3|, given that -2<a<3

|a-4|+|a+3|
-(a-4)+(a+3)

since |a-4|=-(a-4) and |a+3|=a+3 for values of a between -2 and 3.

can you simplify from here: -(a-4)+(a+3)

Answer 29

The hard part is out of the way.

Answer 30

I promise.

Answer 31

You are almost done too I promise.

Answer 32

will it be, -2<a if only -(a-4)<a, and a<3 if only a+4>a.

Answer 33

right?

Answer 34

Oh no what are you doing...

Answer 35

:( I am sorry

Answer 36

You are only looking at the expression -(a-4)+(a+3)

Answer 37

I am not good at math

Answer 38

First distribute.
-(a-4)=?

Answer 39

and you can go ahead and drop the parathesis on the second bunch because there is a + outside
-(a-4)+a+3

Answer 40

can you just do it so i can see pleae?

Answer 41

a(b+c)
=
ab+ac
is the distributive property

Answer 42

you have -(a-4)
or -1(a-4)

Answer 43

=(-1)(a)-(-1)(4)

Answer 44

what is -1(a)?
what (-1)(4)?

Answer 45

I am so confused right now

Answer 46

On multiplying?

Answer 47

isn't it -1a

Answer 48

or -a

Answer 49

and -4

Answer 50

Yes

Answer 51

right so -(a-4)=-a-(-4)

Answer 52

-a-(-4)+a+3

Answer 53

I am sorry i am very confused right now. I am so fool of that and it gives me headache.

Answer 54

Its alright

Answer 55

well first a -(-4) can be written as +4
so you have -a+4+a+3

Answer 56

I know you can add 4 and 3
then also add -a and a

Answer 57

i don't think the problem asked for all that drama thou

Answer 58

what is "giving that -2<a<3

Answer 59

It does ask you to simplify -a+4+a+3

Answer 60

-a+a=?
4+3=?

Answer 61

=7

Answer 62

right

Answer 63

listen, hold om

Answer 64

so how will my solution will be now?

Answer 65

Well you are asked to simplify -a+4+a+3
and you said 7

Answer 66

so what do you mean?

Answer 67

i meant, |a-4|+|a-3|, given that -2<a<3? what is the solution?

Answer 68

I thought it was |a-4|+|a+3|

Answer 69

given -2<a<3

Answer 70

yes

Answer 71

whats is the simplified?

Answer 72

ok so you said since all the values in the interval (-2,3) are less than 4 we would use |a-4|=-(a-4) since this happens when a<4

so we know that we can write |a-4|+|a+3|
as -(a-4)+|a+3| now

you said |a+3|=a+3 since all the values in the interval (-2,3) are greater than -3 we would use |a+3|=a+3 since this happens when a>-3

so now we can write the expression as -(a-4)+(a+3)
Distribute -a+4+a+3
Then combine like terms
-a+a+4+3
0+7
7

Answer 73

okay thank you

Answer 74

i see it.