alainabbyboo22
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
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alainabbyboo22
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ash2326
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@alainabbyboo22 Given that the arcs NM and FM are equal
ash2326
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so chords will be equal too
NM=FM
Can you solve it from here ?
alainabbyboo22
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i'm confused on this . what do i need to do ?
ash2326
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We have the arcs equal as it's indicated in the diagram, isn't it?
alainabbyboo22
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ya
ash2326
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so the chords ( the straight lines ) NM and FM will be equal
NM=FM
alainabbyboo22
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then what do i do ?
ash2326
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You are given the values of NM and FM in the question. Plug them here :
NM=FM
ash2326
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NM=x+40
FM=3x
NM=FM
so
\[x+40=3x\]
Can you solve this @alainabbyboo22 ?
alainabbyboo22
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how do i solve that though ? what do i do ?
alainabbyboo22
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i am sorry if i am irritating you with this but i just don't quite understand this stuff
ash2326
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No problem. I 'll help you figure this out :)
alainabbyboo22
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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 !
ash2326
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We are all here to help. You're welcome
ash2326
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Can you solve this equation for x ?
\[x+4=6\]
alainabbyboo22
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would i take the numbers from the answer choices and plug them into x or would i add 4 + 6 ?
ash2326
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It's just an example, unrelated to the question. Do you know how to solve these type of equations?
alainabbyboo22
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no /:
ash2326
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Ok. I'll explain you
ash2326
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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?
alainabbyboo22
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alright i got that part now !
ash2326
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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 !!
alainabbyboo22
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okay now i'm lost again ..
ash2326
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I'll give you a hint, subtract both sides by x. what would you get?
alainabbyboo22
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the right side would 38 and the left side would be 1 .
ash2326
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What did you subtract?
alainabbyboo22
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am i right ?
alainabbyboo22
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i subtracted 40-2
and 3-2
ash2326
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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?
alainabbyboo22
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3x=40 ?
ash2326
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we have 3x-x, on left side
or
3x-1x, what would you get on the left side?
alainabbyboo22
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x + 38
ash2326
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we have
\[3x-1x=40\]
or
\[x(3-1)=40\]
What would you get next?
ash2326
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what's 3-1 ?
alainabbyboo22
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2
ash2326
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@alainabbyboo22 ?
alainabbyboo22
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i got 2
alainabbyboo22
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where do i go from there now ?
alainabbyboo22
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@ash2326
ash2326
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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?
alainabbyboo22
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yes i see now . okay what do i do to get my answer ?
ash2326
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now what do we have?
alainabbyboo22
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2x = 40
ash2326
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divide both sides by 2, what would you get?
alainabbyboo22
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2 and 20
ash2326
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\[\frac{2\times x}{2}=\frac{40}{2}\]
\[\frac{\cancel 2 \times x}{\cancel 2}=20\]
what would you get for x?
alainabbyboo22
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2
ash2326
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how you would get 2???
alainabbyboo22
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i'm lost .. again .
alainabbyboo22
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would it be 10 ?
alainabbyboo22
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because 20/2
alainabbyboo22
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?
ash2326
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we have
\[2x=40\]
divide both sides by 2 only once
alainabbyboo22
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1x = 20
ash2326
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yeah so x =???
alainabbyboo22
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20 !
ash2326
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good, did you understand this?
alainabbyboo22
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yes now i do ! thank you very much ! (:
ash2326
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Welcome and feel free to contact me here, Anytime for help !!
alainabbyboo22
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thanks !! (: have a great day !