Question

Solve the equation. Check the solution.
-4/x+1 = -1/x+5

Answer 1

\[\frac{ -4 }{ x+1 }=-\frac{ 1 }{ x+5 }\] is it this?

Answer 2

Yes

Answer 3

You could "cross multiply" if you like and then solve for x

Answer 4

\[\frac{ -4 }{ x+1 }=-\frac{ 1 }{ x+5 } \implies -4(x+5)=-1(x+1)\]

Answer 5

No idea how to do any of that lol

Answer 6

okay

Answer 7

Now distribute and solve for x, can you do that

Answer 8

nope I suck at math

Answer 9

multiply through what do you get?

Answer 10

-20?

Answer 11

No, you have to first multiply by x and then 5 so we get \[-4(x+5) = -4x-20\] does that make sense?

Answer 12

okay yes i guess.

Answer 13

Try \[-1(x+1)\] what do you get

Answer 14

-x - 1

Answer 15

right?

Answer 16

Perfect!

Answer 17

We have \[-4x-20=-x-1\] now we can collect "like terms" so the one's with the variables go together and then the ones which are just number are on its own.

Answer 18

okay

Answer 19

How do we do that?

Answer 20

I don't know...

Answer 21

Lets move all the terms with x on the left and the numbers on right, so -4x is already on the left, but notice the -x isn't there, so lets maybe add x on both sides and see what happens, \[-4x-20 \color{red}{+x}=-x-1 \color{red}{+x}\]

Answer 22

Notice it gets cancelled on the right and we're left with the x on the right and we haven't really changed anything other than moving it to the other side :)

Answer 23

okay! so what would i do now to figure out my answer?

Answer 24

\[-4x+x-20=-1\] right now we're solving for x, what should we do next?