Question

How do you solve linear equations that include fractions & variables?

Answer 1

I've gotten this equation,

Answer 2

Hello. Firstly you can multiply whole equation by 9.

Answer 3

I'd multiply by 9 to get rid of the fractions, then move all the x's to one side.

Answer 4

So I get - 27 on the bottom & 54 on the top. Wouldnt the x's on the top cross out?

Answer 5

@gjhfdfg
\[\frac{x-6}{-3} + \frac{x+9}{9} = x+4\]Multiply both sides by 9
\[\frac{x-6}{-3}*9 + \frac{x+9}{9}*9 = 9(x+4)\]Cancel common factors\[-3*(x-6) + (x+9) = 9x + 36\]\[-3x+18+x+9 = 9x + 36\]Collect like terms and solve for x.

Answer 6

Do I subtract 18 from 36?

Answer 7

You can do whatever you want, so long as you do the same thing to both sides of the equation. So, if we want to get all the x terms on the left, subtract any x terms you see on the right from both sides of the equation. \[-3x + 18 + x + 9 = 9x + 36\]Subtract 9x from both sides\[-3x + 18 + x + 9 - 9x = 9x + 36 - 9x\]\[-3x + x - 9x +18 + 9 = 36\]\[-11x + 18 + 9 = 36\]
Now what do you think you should do?

Answer 8

I should add the 9 with the 18 & subtract it from 36?

Answer 9

subtract it from both sides...

Answer 10

very important that you always do the same thing to both sides...

Answer 11

Ah I know, I forgot to put that.
So I came out to get - ( 9 / 11 ) & I believe thats my answer.!
Thank you for your help.!

Answer 12

Good job, that's exactly right!