Question

Which answer shows this equation in standard form?



7 – 3(x – y) = –5x + 2



A.


–8x + 3y = –5


B.


–2x – 3y = 5


C.


2x + 3y = –5


D.


2x – 3y = –5



so, im guessing after we do 7 – 3(x – y) = –5x + 2 its will turn out to be something involved with distributive property.

Answer 1

What i got so far

Answer 2

well standard from is normally

Ax + By = C

or Ax + By + C = 0

so you need to distribute and collect like terms

Answer 3

well that's not good

Id start with

7 - 3x + 3y = -5x + 2

I did this by distributing the 3

now you can collect like terms...

Answer 4

I'm confused on what operations to do for them...I gave it my best shot. @campbell_st

Answer 5

:3 @jim_thompson5910

Answer 6

you can't go from `7 – 3(x – y) = –5x + 2` to `4(x – y) = –5x + 2`

you have to distribute first, then combine like terms

Answer 7

I thought she already distributed when campbell said " I did this by distributing the 3"

Answer 8

May I interject something that may help here?

Answer 9

go ahead

Answer 10

So do you know the order of operations gabby?

Answer 11

Yes. PEMDAS

Answer 12

Good, so, when you are trying to get a variable by itself, you actually can use the reverse order of ops as a guide as to what steps to take. I call it SadMep (look familiar?)

Answer 13

So, in this situation, you want to have only x and ys on the left. yea?

Answer 14

Yes...

Answer 15

ok, so this one has parentheses right?

Answer 16

yes.

Answer 17

ah, sorry, I want to follow sadmep. not do multiples, ignore the parentheses thing

Answer 18

ok, so do we have any x's or y's on the right?

Answer 19

Yes. Only 5x.

Answer 20

alright, and is it being S or A?

Answer 21

We are following SadMep

Answer 22

A

Answer 23

good, so how do we undo addition?

Answer 24

With subtraction.

Answer 25

yes, subtraction from Both sides though yea?

Answer 26

Yes.

Answer 27

So,

Answer 28

so if you do that subtraction, we get
\[7 – 3(x – y) = –5x + 2\\7 – 3(x – y) -(-5x)= –5x -(-5x)+ 2\\7-3(x-y)-(-5x)=2\]

Do you agree?

Answer 29

Why do we still have 5x. I thought it got cancelled out.

Answer 30

ah, not quite. So 1. you are subtracting -5x from both sides. 2. both sides means both the left side of the equals sign and the right side of the equals sign

Answer 31

we just want to move the \(\color\red{-}5x\) to the other side. that was our goal.

Answer 32

very important to keep that minus sign too

Answer 33

Hmm, okay. By doing that we subtract....

Answer 34

well, subtracting a negative is the same as adding the positive. It cancels out

Answer 35

Oh. :3

Answer 36

so when you do these problems. Write them out as I did above. Use full 'sentences'

Answer 37

it will help minimize confusion

Answer 38

so we are here: \[7−3(x−y)−(−5x)=2\]

Answer 39

now using SadMep to decide what you should do first, can you tell me the next step?

Answer 40

Well since we already do subtraction, we add now...but there is nothing to add o-o

Answer 41

well, not quite, you actually restart the algorithm every time. So remember our goal of only having x and y terms on the left? Do we have any items that are not x or y over there currently?

Answer 42

Yes. 7 & 2.

Answer 43

the two is on the left side?

Answer 44

No, right...my bad.

Answer 45

it's cool, so that 7 though what is it doing? we don't want it there, we need it over on the right hand side. How can we get it there?

Answer 46

By doing 5x+2-7?

Answer 47

uhm, that doesn't make sense. Remember we want to use full sentences. so you are here:\[7−3(x−y)−(−5x)=2\]

Answer 48

what do you need to to to both sides in order to move the 7 to the right side?

Answer 49

why did you tuck that little -7 by the 3?

Answer 50

I wanted to squeeze the -7 in but not make it overlap the parenthesis or the x

Answer 51

So the way you are currently doing it, you changed the problem to:
\[-3-7(x-y)-(-5x)=2\] That is actually a completely different problem
remember you need to do it to both sides. That means once from the left hand side of the equals sign and once from the right.

Answer 52

Well... this would be my only other guess

Answer 53

and that would be correct

Answer 54

:D Hazaa!

Answer 55

now, simplify what you can on each respective side using PEMDAS.

Answer 56

tell me what you get

Answer 57

I was thinking that I could use like terms and do x- 5x but there's probably no way.

Answer 58

so you dropped the minus from the minus minus 5x again. Right hand side looks good. Now, this is where wayyyyyyy up at the top I stepped in

Answer 59

This is the distributive property part. To which, I let @campbell_st or @jim_thompson5910 complete their thoughts.

Answer 60

Okay, thanks for the help so far. :)

Answer 61

so you are here guys: \[-3(x-y)-(-5x)=-5\]

Answer 62

np :)

Answer 63

Standard Form: the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

http://jwilson.coe.uga.edu/emt668/emat6680.2002/jackson/chapter%205%20lesson%20plan/day6.html

Answer 64

I was told that earlier by FibonacciChick666, but I don't get how that will help me solve the problem.

Answer 65

(it is the template for how you want to make the problem look) Your goal is to have 3 terms total an x term with a coefficient, a y term with a coefficient, and a term that is just a number.

Answer 66

okay.

Answer 67

if the notation `Ax + By = C` confuses you, then think of standard form as this (in the drawing below)