What is the Equation in Fraction Form for Solving a Linear Equation?

[Paulo2014]

Homework Statement

(3x-5)/4 + (2-3x)/2 = (x-2)/5

Homework Equations

The Attempt at a Solution

I tried this and got x= 6.3 reacurring... but i don't think it is right...

 

[rocomath]

$$\frac{3x-5}{4}+\frac{2-3x}{2}=\frac{x-2}{5}$$

Multiply everything by 20

$$5(3x-5)+10(2-3x)=4(x-2)$$

Take it from here ...

 

[Snazzy]

Show your work, how did you get that answer?

 

[Paulo2014]

I multiplied everything by 40, not 20, and then went 10(3x-5) + 20(2-3x) = 8(x-2)

 

[rocomath]

Ok, keep showing your work and we'll look over it. I'm not going to do it for you.

You can check if your solution is correct by plugging it into your original equation ... left should equal the right.

 

[Paulo2014]

I know. then I expanded everything to make it :
30x-50+40-60x=8x-16

Then I combined like terms to make it -30x-10=8x-16

Then I moved like terms to make it: -38x=-6

Which equals 6.3 reacuring... is that right?

 

[rocomath]

Work looks fine, now check your solution.

 

[Snazzy]

Why are you dividing 38 by 6? You're trying to solve for the x.

 

[Paulo2014]

Don't you divide by the number in front of x by the number after the equals sign to get the answer for x?

 

[Snazzy]

No. For example:

$$6x = 12$$

$$\frac{6x}{6}=\frac{12}{6}$$

$$x=2$$

This is really basic algebra.

 

[Paulo2014]

But that is exactly what I did... -38x/-38= -6/-38

 

[Snazzy]

6/38 is not 6.333.

 

[Paulo2014]

oh... i see what i did wrong... thanks for pointing that out...