# Solve linear equation

• Feb 21st 2010, 02:06 AM
math934
Solve linear equation
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.
• Feb 21st 2010, 02:46 AM
jgv115
I'm really confused by your method and I'm sure you are confusing yourself. Make it easier by taking away 1 thing at a time:

Expand brackets to get:

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

Get the x values to the left side.

$-15-10+15x+3 = -20+13$ I added 16x to both sides.

Now the rest should be simple.

You are doing this:

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

See how you just wrote "16x" you may as well add it straight away to get yourself not confused...
• Feb 21st 2010, 03:18 AM
HallsofIvy
Quote:

Originally Posted by math934
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

Here's your error. You added 10- 3 to both sides but the right side is -20+ 13. You dropped the -20.

Quote:

0 = 20
You should have 0= 20- 20 which is the same as 0 = 0.

Quote:

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.
• Feb 21st 2010, 04:31 PM
math934
re:
HallsofIvy,
I knew it,I knew it, I knew it. This is my problem. I always make the silliest mistake and end up messing up the entire problem

Thanks very much for your help.