-7p/14 +11/8=6p/12+24/4

Question

not sure what to do with denominators...

Answer 1

-7p + 11 = 6p + 24

 14      8     12     4

 

Assuming the question is to find 'p', first we need to find the common denominator for the fractions.

 

 

 

-84p + 231 = 84p + 1,008

 168     168    168      168

 

Nothing divides evenly by both 12 and 14, except 168, the product of multiplying them together.

If we change the denominators via multiplication to make them all match, we must also multiply the numerator by the same number used to make the denominators match.

 

 

 

231 = 168p + 1,008

168     168        168

 

To find a variable, isolate it to one side. Add 84p/168 to both sides.

 

 

 

-777 = 168p

 168      168

 

Subtract 1,008/168 from both sides.

 

 

 

Divide to solve: p = -4.625.

 

Answer 2

We'll have to find the least common denominator.  To do that let's factor each of our denominators to their smallest factors:

 

14 = 7•2

8 = 2•2•2

12 = 3•2•2

4 = 2•2

 

Now we'll collect the least part of each.

7•2•2•2•3 = 168

Note that we can divide 168 by 14, 8, 12, or 4.

 

So we can multiply each term by 168 to cancel each of the denominators.

 

This gives:

 

-7(12)p + 11(21) = 6(14)p + 24(42)

 

This gets rid of all of the denominators

 

Solving for p will give the same answer of -4.625