Hi,

I found the following practice problem online. I tried to solve it by doing what I was taught at school to solve such an equation-moving the variable to one side and the constants to another and I ended up with this:

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

-15x -10 -x + 3 = -16x -20 + 13

-15x -x +16x = 10 -3 +13

0 = 20

Obviously wrong!

But actually solution does this:

5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

-15x -10 -x + 3 = -16x -20 + 13

-16x -7 = -16x -7

Multiply both sides by 16x + 7 and get:

0=0

Why does the conventional method not yield results when that is how I solve all my linear equations? How do I know when to apply the second method?

Thanks.