could someone help with fractions?

Question

1/3x-1/4x=1/2-1

Answer 1

1/3x - 1/4x = 1/2 -1

 

One way to solve this is multiply both sides of the equation by 12. 12 is a common multiple of 3,4 and 2.

 

We get: 12/3x - 12/4x = 12/2 - 12

 

This reduces to: 4x - 3x = 6 -12

 

simplifying more: x = -6

Answer 2

Hi Seth,

 

There are 2 parts to your problem.  First lets figure the answer to the right of the equals.

 

1/2 - 1 = ?

 

What does 1 equal?

1 = 2/2

so 1/2 - 2/2 = 1-2 halves.

1/2 - 1 = -1/2

 

Now...

How can we substract 1/4x from 1/3x?

We need a common denominator.

 

Our lowest common denominator is 12.

1/3 = 4/12

1/4 = 3/12

 

So...

4/12x - 3/12x = -1/12x

 

Now we know this:

1/12x = -1/2

 

Let's solve for x by isolating x.  We do this by multiplying both sides by 12 (which is the inverse of 1/12).

 

1/12x = -1/2

(12)(1/12)x = (-1/2)(12)

x = (-1/2)(12)

 

What is half of 12?

x = -6

Let's check our work.

1/3x - 1/4x = -1/2

What is 1/3 of -6 and 1/4 of -6?

1/3 * -6 = -2

1/4 * -6 = -1.5 (3/2)

-2 + 1.5 = -1/2

 

This is true so our answer is correct.  x = -6