Question

What is 0.5(x-3)+(1.5-x)=5x

Answer 1

Simplify what needs to be simplified. That begins by getting rid of the parentheses.

Answer 2

(correctly, of course)

Answer 3

So I distribute 0.5 first?

Answer 4

Yes.
And as for the +(1.5 - x) bit, that's like distributing 1, which just means, get rid of the parentheses :)

Answer 5

So you will get 0.5x-1.5+1.5-x+5x

Answer 6

You mean = 5x at the last bit, right?
typo?

Answer 7

Yes = 5x .. huge typo

Answer 8

0.5x-1.5+1.5-x = 5x
Okay, can you take it from here?

Answer 9

I can but what is 0.5x-x ..

Answer 10

Ahh... I see where this might be confusing... you want to multiply both sides by 10?

Answer 11

It doesn't change the answer, but it might make it easier for you...

Answer 12

Both sides of the equal side?

Answer 13

Yes, of course. It's only fair :)
Multiplication property of equality...

Answer 14

So 0.5x times 10 will become 5x then subtract by x it will equal 4x?

Answer 15

Whoops... you also have to multiply the x by 10.
You multiply EVERYTHING by 10 so that the equality remains.

Answer 16

Aww okay .. So how would I write the whole equation out?

Answer 17

\[\Large 0.5x-1.5+1.5-x = 5x\]
\[\Large \color{red}{10}(0.5x-1.5+1.5-x) =\color{red}{10}( 5x)\]

We just multiplied 10 on both sides... not really necessary, but it makes it easier to solve :)

Answer 18

So, distribute on the left, multiply on the right, what do you get?

Answer 19

5x-15+15-10x=50x

Answer 20

Yeah, does that allay your confusion? :)

Answer 21

Yes .. A lot!!

Answer 22

Okay, try solving it now :)

Answer 23

When I get down to -5x=50x I just divide?

Answer 24

You can't, because they both have x.
You have to bring all numbers with x to one side.

Answer 25

err... all *terms* with x.

Answer 26

Soo how again do I that.

Answer 27

Well, Let's bring the -5x to the right side... it's a minus, so what do we do to get rid of it?

Answer 28

Add it on both sides

Answer 29

Add...what?

Answer 30

-5x

Answer 31

No, that gets you nowhere...
-5x -5x = 50x - 5x
-10x = 45x

Answer 32

Okay that solves everything .. I'm finally good now

Answer 33

okay... if you're sure... what's your answer?

Answer 34

Should I get a zero for 0=4.5x .. this is what my teacher got last period.

Answer 35

Yes!
That is correct ^_^

Answer 36

Omg .. Yes!! .. I feel so smart now lol!

Answer 37

I'm sure you are :D

Answer 38

Thank you!