Question

Calculate the value of x, given line segment FM = 3x and line segment MN = x + 40.

A. 13.3
B. 10
C. 40.
D. 20

Answer 1

@alainabbyboo22 Given that the arcs NM and FM are equal

Answer 2

so chords will be equal too
NM=FM
Can you solve it from here ?

Answer 3

i'm confused on this . what do i need to do ?

Answer 4

We have the arcs equal as it's indicated in the diagram, isn't it?

Answer 5

ya

Answer 6

so the chords ( the straight lines ) NM and FM will be equal
NM=FM

Answer 7

then what do i do ?

Answer 8

You are given the values of NM and FM in the question. Plug them here :
NM=FM

Answer 9

NM=x+40
FM=3x
NM=FM
so
\[x+40=3x\]
Can you solve this @alainabbyboo22 ?

Answer 10

how do i solve that though ? what do i do ?

Answer 11

i am sorry if i am irritating you with this but i just don't quite understand this stuff

Answer 12

No problem. I 'll help you figure this out :)

Answer 13

thanks so much ! (: i really appreciate it ! thank you for taking your time out of your day to try and help me out on this !

Answer 14

We are all here to help. You're welcome

Answer 15

Can you solve this equation for x ?
\[x+4=6\]

Answer 16

would i take the numbers from the answer choices and plug them into x or would i add 4 + 6 ?

Answer 17

It's just an example, unrelated to the question. Do you know how to solve these type of equations?

Answer 18

no /:

Answer 19

Ok. I'll explain you

Answer 20

Her we have
x+4=6
it means that x+4 is equal to 6
x is a variable, we need to find its value which will make this equation true. There is only one value of x which will make this equation true. It's easy to find that :)
We need to modify it in such a way that we have x separate and no or no.s separate.
\[x+\underline 4=6\]
I can see that 4 is on left side. Want to remove it !!
So I subtract both sides by 4, it's important to remember that whatever operation I do be it add, subtract, multiply or divide. I have to do on both sides not one side
\[x+4-4=6-4\]
Now I'll simplify
\[x+\cancel 4- \cancel 4=2\]
\[x+0=2\]
or
\[x=2\]
Do you get this?

Answer 21

alright i got that part now !

Answer 22

good, similarly we have to find the value of x here.
We know
FM=MN
so
\[3x=x+40\]
here x on the right side is to be removed, what can you do remove x from right side?
remember operations on both sides !!

Answer 23

okay now i'm lost again ..

Answer 24

I'll give you a hint, subtract both sides by x. what would you get?

Answer 25

the right side would 38 and the left side would be 1 .

Answer 26

What did you subtract?

Answer 27

am i right ?

Answer 28

i subtracted 40-2
and 3-2

Answer 29

You made a mistake somewhere. No worries, I'll guide you
\[3x=x+40\]
subtract both sides by x, because we want to remove x from the right side
\[3x-x=x+40-x\]
Now what would you get?

Answer 30

3x=40 ?

Answer 31

we have 3x-x, on left side
or
3x-1x, what would you get on the left side?

Answer 32

x + 38

Answer 33

we have
\[3x-1x=40\]
or
\[x(3-1)=40\]
What would you get next?

Answer 34

what's 3-1 ?

Answer 35

2

Answer 36

@alainabbyboo22 ?

Answer 37

i got 2

Answer 38

where do i go from there now ?

Answer 39

@ash2326

Answer 40

so you have
\[x \times 2=40\]
If you subtract variables, like 4x-2x
just subtract 4-2=2 and put the 2 before x
but if you have x-x or 9x-9x it'll become 0
do you get this?

Answer 41

yes i see now . okay what do i do to get my answer ?

Answer 42

now what do we have?

Answer 43

2x = 40

Answer 44

divide both sides by 2, what would you get?

Answer 45

2 and 20

Answer 46

\[\frac{2\times x}{2}=\frac{40}{2}\]
\[\frac{\cancel 2 \times x}{\cancel 2}=20\]
what would you get for x?

Answer 47

2

Answer 48

how you would get 2???

Answer 49

i'm lost .. again .

Answer 50

would it be 10 ?

Answer 51

because 20/2

Answer 52

?

Answer 53

we have
\[2x=40\]
divide both sides by 2 only once

Answer 54

1x = 20

Answer 55

yeah so x =???

Answer 56

20 !

Answer 57

good, did you understand this?

Answer 58

yes now i do ! thank you very much ! (:

Answer 59

Welcome and feel free to contact me here, Anytime for help !!

Answer 60

thanks !! (: have a great day !