# Equations - both addition and multiplication

• Feb 24th 2006, 08:58 AM
Euclid Alexandria
Equations - both addition and multiplication
45 = -10 - y

Here is how I tried to solve the problem. Judging from the section of the book I'm working in, there should have been some multiplication involved.

45 + 10 = -10 - y + 10 (Add 10 to both sides.)
55 = y

By checking the original equation, I came up with a false statement.

45 = -10 - 55
45 = -65

Any hints?
• Feb 24th 2006, 09:12 AM
ThePerfectHacker
Quote:

Originally Posted by Euclid Alexandria
45 = -10 - y

Here is how I tried to solve the problem. Judging from the section of the book I'm working in, there should have been some multiplication involved.

45 + 10 = -10 - y + 10 (Add 10 to both sides.)
55 = y

By checking the original equation, I came up with a false statement.

45 = -10 - 55

45 = -65

Any hints?

After you add 10 to both sides you have,
\$\displaystyle 55=-y\$
Not \$\displaystyle 55=y\$.
Now multiply by negative one to get,
\$\displaystyle -55=y\$
• Feb 25th 2006, 01:10 PM
Euclid Alexandria
Thanks for pointing out my mistake. Will multiplying by the variable on the other side work in every case? My book's example problem solves by dividing each side by -1.
• Feb 25th 2006, 01:57 PM
topsquark
Quote:

Originally Posted by Euclid Alexandria
Thanks for pointing out my mistake. Will multiplying by the variable on the other side work in every case? My book's example problem solves by dividing each side by -1.

Multiplying both sides of an equation by -1 gives the same result as dividing both sides by -1. It just depends on your philosophical methodology. :D

-Dan
• Feb 26th 2006, 08:38 PM
Euclid Alexandria
Thanks! :)