Question

Given the equation 2(3x − 4) = 5x + 6, solve for the variable. Explain each step and justify your process.
Charlie solved a similar equation below. Is Charlie's solution correct? Explain why or why not.
4x − 3 = 2(x − 1)
4x − 3 = 2x + 2
2x − 3 = 2
2x = 6
x =3

Answer 1

Let's do the first question. Can you distribute 2 in 2(3x-4)

Answer 2

What even is this sorcery

Answer 3

Let's take it step by step

So we need to distribute. I'll show you an example so you can understand

5(3x-6)
= (5*3x) - (5*6)
= 15x - 30

Now can you do the same for
2(3x-4)
@animeghoul8863

Answer 4

2(3x − 4) = 5x + 6
Step 1: (2*3x) - (2*4)

Answer 5

^like that

Answer 6

2(3x − 4) = 5x + 6
Step 1: (2*3x) - (2*4) =6-8

Answer 7

Don't bother with writing steps, just do as I say and I'll show you how to write it all together

Answer 8

So you made a mistake
2*3x = 6x

You can't forget that x, it's a variable and needs to stay

Answer 9

2(3x − 4) = 5x + 6
(2*3x) - (2*4) =6x-8
6x-8=5x+6

Answer 10

Good good, we're on the right track now

Answer 11

2(3x − 4) = 5x + 6
(2*3x) - (2*4) =6x-8
6x-8=5x+6
+8 +8
simplify
6x=5x+14
-5 -5
x=14

Answer 12

^^^^^ hows that *pant pant pant*

Answer 13

Uh-oh, slight mistake

You were subtracting 5x not 5
But then next step is correct that x=14

Think of it like this
that the 'x' is an apple

I have 5x or 5 apples
If you give me some apples so that I now have twice as.many apples I have 2*5x or 10apples
And then you decide to give me their number 2. It's just a number
That means I have 10x + 2
Not 12x, not 12
I don't have 12 apples or my apples don't disappear into a random number

Does that make sense
But you're getting a good grasp on things so far, so good job!!

Answer 14

Your profile picture is so confusing because it looks like you're typing

Answer 15

2(3x − 4) = 5x + 6
(2*3x) - (2*4) =6x-8
6x-8=5x+6
+8 +8
simplify
6x=5x+14
-5x -5x
x=14

Answer 16

so as long as it looks like this its correct

Answer 17

I guess it's fine, that format would look much better if it's written on paper tbh

Answer 18

im sorry but im homeschooled and have to hand it in online i cant put it on paper but would it be correct if i kept it this way

Answer 19

Yeah I know, that way should be fine. Your teacher should understand it

Answer 20

ok part B

Answer 21

Yes, what mistakes did you catch

Answer 22

2x − 3 = 2

Answer 23

Also look at 2(x-1) what should 2(x-1) be

Answer 24

4x − 3 = 2(x − 1) <<<<<< 2x-1?
4x − 3 = 2x + 2
2x − 3 = 2<<<<<<< because 4x-3=2x+2 simplified = 5
2x = 6
x =3

Answer 25

Also we should always try to find the first mistake done because that's were it got derailed first

Answer 26

It should be 2x-2

You have to multiple the 2 across and a minus

Answer 27

4x − 3 = 2x-2
4x − 3 = 2x + 2
2x − 3 = 2<<<<<<< because 4x-3=2x+2 simplified = 5
2x = 6
x =3

Answer 28

so like that

Answer 29

Err
We need to work on distributing

Solve these random questions. You really need to understand this because this is a basic concept
2 different questions
2(4x + 7) =
2(4x - 7) =

Answer 30

(2*4x)+(2*7)=8x+14=22
(2*4x) - (2*7)= 8-14=6

Answer 31

@TheSmartOne

Answer 32

Ahh
That's where you're messing up

You can't add apples and oranges
8x+ 14 stays as 8x + 14
8x has an x, 14 does not
You cannot add them

Does that make sense

Answer 33

yes

Answer 34

Good, now distributing isn't that easy so let me give you another question so you can handle the other type

-5(x-4) =
-5(x+4) =

Answer 35

ummmmmmm i dont know i havent done this i dont think

Answer 36

It's ok, it's practically the same except now we have a negative

Which means we have to distribute them negative sign as well which means sign flips inside

Answer 37

4x − 3 = 2x-2
4x − 3 = 2x - 2
+3 +3
simplify
4x=2x+1
-2x -2x
simplify
2x=1

Answer 38

how did i do this time :3

Answer 39

did i do it correctly

Answer 40

@TheSmartOne

Answer 41

4x − 3 = 2x-2
4x − 3 = 2x - 2
+3 +3
simplify
4x=2x+1
-2x -2x
simplify
2x=1
x=1/2 or .5

Answer 42

@TheSmartOne

Answer 43

TSOOO NOOO HE WAS TOOOO YOUNG!!!!!!!!!!!!!!!!!!!

Answer 44

@Shadow

Answer 45

i think TSO died

Answer 46

You solved it correctly, now compare it to Charlie's and see what he did wrong