Question

-17 – x = -2(3x + 1)

Answer 1

You need to distribute the -2 to each of the terms in the parentheses. Then you can solve it in the usual way.

Answer 2

i did that polPak and heres what i came up with

Answer 3

-21

Answer 4

Nope. What was the equation after you do the distributing?

Answer 5

-17 - 6x +6X -2-X

Answer 6

2(3X +1)
-17- X= 6X + 2

Answer 7

You forgot that it's a -2, not 2 you're distributing.

Answer 8

\[-2(3x + 1) = -2(3x) -2(1) = -6x - 2\]
So you should have
\[17 - x = -6x -2\]

Answer 9

oh so the 6 becomes -6x

Answer 10

And the 2 becomes -2.

Answer 11

Err My equation is slightly wrong..

You should have \[-17 -x = -6x -2\]

Answer 12

-17 - x = -6 - 2

Answer 13

Don't lose track of the x on the -6. It's important

Answer 14

then now i can solve for x
so the its
-17x -6 - 2

Answer 15

No. -17 - x is not -17x and you can't just put them together like that.

Answer 16

Ok look at it like this.

Answer 17

ok

Answer 18

You have this equation:
\[-17 - x = -6x -2\]

That means that \(-17 - x\) IS EXACTLY THE SAME AS \(-6x -2\)

So if they are the same then isn't \((-6x -2) + 2\) exactly the same as \((-17 - x) + 2\)?

Answer 19

-17 - 8 so there for x is 8

Answer 20

I have no idea what you are doing.. -17 - 8 doesn't enter into it.

Answer 21

i am just lost

Answer 22

Ok stop doing things.. Just look at what I'm saying.

Answer 23

\[-17 - x \text{ EQUALS } -6x -2\]

Answer 24

okay lol i am stopping right now

Answer 25

Ok? They are the same.

Answer 26

That's what equals means right?

Answer 27

yes

Answer 28

Ok so now lets use some basic arithmetic rules to clean this up a bit.

First we can swap the terms on the left because addition can be rewritten in any order and it works the same..
\[-17 -x = -x -17\] right?

Answer 29

okay

Answer 30

Do you agree that those two are equal? Is 3+5 the same as 5+3 and -3 - 5 the same as -5 - 3?

Answer 31

yes

Answer 32

because you distribute right

Answer 33

Commute, but yeah.

Answer 34

Ok, so -17 - x is the same as -x - 17.

But we also said that -17 - x was the same as -6x - 2.

So that means that -x - 17 must be the same as -6x - 2.

Answer 35

Right?

Answer 36

right

Answer 37

So now our equation looks like this:
\[-x - 17 = -6x - 2\]

Answer 38

that part i got is solving for x thats has me upside ways

Answer 39

We'll get there.

Answer 40

So if those two things are the same.. Then isn't \[6x + (-x - 17) = 6x + (-6x - 2)\]

Answer 41

Because we added 6x to both sides, and if they were equal to start with, they must still be equal.

Answer 42

okay thats the part that throws me off

Answer 43

How so?

Answer 44

its like my flipping mind goes blank and i have no idea what comes next

Answer 45

Ok relax for a second and lets talk about something else first.

Answer 46

or maybe i am trying too hard to understand and i get tied up

Answer 47

Think of a number, any number you want. Don't tell me what it is.

Answer 48

ok

Answer 49

Now, tell me what 2 times that number is.

Answer 50

184

Answer 51

Ok. So now I will magically read your mind and tell you that your number is 92!

Answer 52

How did I accomplish this sorcery?

Answer 53

lol yes

Answer 54

you divided

Answer 55

But how does that help me?

Answer 56

Because you told me that 2x = 182

Answer 57

Well I know that if 2x = 182 then \[2x \times {1 \over 2} = 182 \times {1 \over 2}\]

Answer 58

so you have to find out what 2x amounts to

Answer 59

Because you said that they were the same, so anything I do to both sides will maintain equality.

Answer 60

And \[2x \times \frac{1}{2} = x\]

Answer 61

And \[182 \times \frac{1}{2} = 92\]

Answer 62

So therefore x = 92

Answer 63

So now I'm thinking of a number.

Answer 64

91

Answer 65

okay

Answer 66

Whoops. Sorry I typo'd your response.

Answer 67

Shoulda been 184 not 182.

Answer 68

no one has ever broke it down like this thank you

Answer 69

its okay

Answer 70

so you want me to solve for your number

Answer 71

Now if you take the number I'm thinking of, and add 17 to it. You will get 2 more than 6 times that same number.

Answer 72

So first. can you write an equation (using x for my number) which describes the statement I've given you?

Answer 73

2(6^6)+17=X

Answer 74

Not quite. Lets break down what I said:

x + 17
The number I'm thinking of, and add 17 to it

=
IS

2 more than 6 times that number
2 + 6x

Answer 75

Or better still
6x + 2

Answer 76

12(6)=72+17=89

Answer 77

No no no.

Answer 78

OH WOW

Answer 79

You keep jumping ahead ;)

Answer 80

okay am slowing down

Answer 81

and laughing at myself

Answer 82

np =)

Answer 83

Try again.

14 more than the number is 2 more than 4 times the number.

Answer 84

We're just practicing turning english into equations.

Answer 85

okay

Answer 86

Don't try to solve it yet. Just rewrite what I say in equation form.

Answer 87

Actually 14 more than the number is 5 more than 4 times the number.

Answer 88

14 + n = 2(4)

Answer 89

Sorry

Answer 90

Almost!

Answer 91

was i close

Answer 92

The left side is right, the right side is not.

Answer 93

Try my last version, but break it down a bit.

If x is my number what is 4 times my number??

Answer 94

14 + n = 5(4 + n) oh please be right

Answer 95

You're doing great btw. It's important to have patience when working through this.

Answer 96

No, that's not right still. Lets work through it a little at a time.

Answer 97

What is 4 times my number?

Answer 98

your number is 14 right