Question

Are the equations 3x = -9 and 4x = -12 equivalent?

Answer 1

What is the solution for x in the first equation?
What is the solution for x in the second equation?

Answer 2

does x in the first equation equal -12?

Answer 3

i think im entirely confused

Answer 4

and then the second equation -16?

Answer 5

Are you having problems solving for x?

Answer 6

yeah

Answer 7

Ok, here's how you set that up and we can solve it together.

Answer 8

okay thank you

Answer 9

3x = -9
The first thing you have to realize or remember is that multiplication and division are opposites of one another, just like addition and subtraction are opposites of one another. So if you want to "undo" multiplication, you use division. In our case, we have a 3 multiplied by an x to give us 3x.

Answer 10

ohhh

Answer 11

3x is 3 times x. You got that, right?

Answer 12

yeah

Answer 13

The job you are given here is to see if those equations are equal to one another, and in order to do that you have to solve each of them for x. That means that you have to end up with x = something. You have to get x alone. Right now the x has a 3 stuck to it by multiplication. So we have to do something about that 3. Since it is multiplied in, we need to divide it away, cuz division is the "undoing" of multiplication. That is done like this:
\[3x=-9\]
\[\frac{ 3x }{ 3 }=\frac{ -9 }{ 3 }\]

Answer 14

There are 2 things that happened right there. First of all, on the left side, the fact that you have a 3 in the top and a 3 in the bottom cancels them out so you're left with just x, which is what we are aiming for. Secondly, you MUST remember that in an equation, meaning anything that has an equals sign in, if you do one thing to one side you HAVE to do it to the other side. So we divided the 3 away on the left, and we also have to divide the other side by 3.

Answer 15

3 divided by three is 1????

Answer 16

What we are left with is this:
\[x=-\frac{ 9 }{ 3 }\]
which can be divided to equal -3. So we know that x here is -3.

Answer 17

Yes, 3/3 = 1.

Answer 18

Now let's do the same thing with the other one. Let's see what x is equal to

Answer 19

4x = -12
Divide BOTH sides by 4 to "undo" the mutiplication of 4x:
\[\frac{ 4x }{ 4 }=-\frac{ 12 }{ 4 }\]

Answer 20

x = -3 on both

Answer 21

The 4's on the left cancel out, leaving you with
\[x=-\frac{ 12 }{ 4 }\]

Answer 22

Yes! -3 on both! So they are equal! Good job!

Answer 23

thank you