Solve the equation Check the solution.
−2/x+4 = 4/x+3

Question

Solve the equation Check the solution.
−2/x+4 = 4/x+3

johnweldon1993 · Answer

$$\large \frac{-2}{x + 4} = \frac{4}{x + 3}$$

like that right?

anonymous · Answer

$$\frac{ -2 }{ x+4 } = \frac{ 4 }{ x+3 }$$

anonymous · Answer

yes!

johnweldon1993 · Answer

Alright lol....well we can begin by cross multiplying!

anonymous · Answer

everyone alsways wants to solve the cute girls question lol

anonymous · Answer

sooo multiply -2 and what? lol

johnweldon1993 · Answer

|dw:1400708614593:dw|

like that

johnweldon1993 · Answer

So it would be -2 times the (x + 3)    and also the 4 times the (x + 4)

so now we will have

$$\large -2(x + 3) = 4(x + 4)$$

right?

anonymous · Answer

ohhh. okay okay i see. one sec

anonymous · Answer

okay whats next

johnweldon1993 · Answer

Well now we solve for 'x'

Start by distributing the -2 and the 4 into those parenthesis...

anonymous · Answer

ummm....x+-6 = x+24

anonymous · Answer

??

johnweldon1993 · Answer

Not quite....so we had

$$\large -2(x + 3) = 4(x + 4)$$

right? so what we do...is distribute the -2 into those parenthesis...

We take the -2....and multiply it by every term inside the parenthesis...so we will have

$$\large -2x - 6 = 4(x + 4)$$

make sense? and now we do the same thing for the 4...

anonymous · Answer

ohh duh. lol 
so -2x-6 = 4x+24

johnweldon1993 · Answer

Hmm....4 times 4 is what again?

anonymous · Answer

omg..wow.  16

johnweldon1993 · Answer

haha you're doing good ;P

Alright great! so we have

$$\large -2x - 6 = 4x + 16$$

Now to combine like terms...we want all the terms with an 'x' on 1 side of the equation....and the other ones on the other side

johnweldon1993 · Answer

We can do that by adding 2x to both sides of the equation....and then subtracting 16 from both sides of the equation...

what do we have after doing that?

anonymous · Answer

divide -22by6

johnweldon1993 · Answer

Yes! which is?

anonymous · Answer

-3.7

anonymous · Answer

i need it to be an improper fraction

johnweldon1993 · Answer

Great!...so we know that

$$\large x = -3.7$$  now we check it...

And oh okay...then -22/6 it is....but that can be simplified a bit right?

anonymous · Answer

wait.. how did you get the improper fraction?

johnweldon1993 · Answer

Remember how you said the next step would be

"divide -22 by 6" ? :)

johnweldon1993 · Answer

That is the fraction...

$$\large x = \frac{-22}{6}$$

anonymous · Answer

yes i know but how to you turn -3.7 into an improper fraction...

anonymous · Answer

i understand that -22/6 IS the improper fraction. but how did you get that

johnweldon1993 · Answer

I'm not sure what you mean...

alright...lets put it like this...

We knew to solve for 'x'....we would divide -22 by 6

When you DO divide -22 by 6...you get the -3.7    

$\large \frac{-22}{6} = $improper fraction version

when you actually DO -22 divided by 6...you get $\large -3.7 =$ decimal version

johnweldon1993 · Answer

the only thing that we did...was  go back 1 step...

instead of actually doing the calculation of  -22/6      (which comes out to the -3.7 you said)

we just left it as the -22/6

anonymous · Answer

ohhhh >_< okay okay

johnweldon1993 · Answer

lol don't worry about it hun you're fine :)

alright...alright....we have

$$\large x = \frac{-22}{6}$$ right? but...that can be simplified a bit (not calculated...but simplified)

anonymous · Answer

-11/3

anonymous · Answer

and thats my answer. right?

johnweldon1993 · Answer

Perfect! that is your improper fraction...and that is your answer :)

anonymous · Answer

can you help me with another?

anonymous · Answer

im gonna tag you in the question