equation balance

SOLVING ax + b = c

Otherwise known as:

"The Great Mathematical Balancing Act"

this is sylvia the super solver Here is Sylvia the SUPER SOLVER.
She is sooooo good at solving equational mysteries that
she can do them blindfolded. Her only help in these
mathematical matters is her every ready PAN BALANCE.

Now actually we think that all great mathematicians
should own one of these balance things. They are
great. Just look at the Algebra they can solve for you.

Here is an example:

Suppose the left pan of the balance holds 3 mystery folders
and 4 one ounce weights. Now this is balanced on the right
side with 13 one ounce weights.

dddd 111 = ddddddddddddd

Now Sylvia says, "I will remove the 4 one ounce weights
from the left pan, and to balance this, I will also remove
four one ounce weights from the right pan."

111 = ddddddddd

This leaves her with three mystery folders equaling
nine ounces total.

She says to herself at this point, "If three mystery folders
are exactly equal to 9 ounces, then one third (1/3) of the
folders will equal one third of the 9 ounces."

1 = ddd

Thus one mystery folder weighs exactly 3 ounces!
WAY TO GO SYLVIA!

*Sylvia knows that the key to solving for the
mystery folder is to work her way down to just
ONE folder, always remembering to keep the
pans balanced as she works.

The Algebra of Sylvia's pan balance looks like this:

3x + 4 = 13

3x + 4 + -4 = 13 + -4 (addition property of equality)

3x = 9

3x = 9 ( division property of equality )
3 3

1x = 3

We recently found this great electronic balance beam that lets
you solve all kinds of linear problems with integers.

You can make up your own, or let the computer generate them for you.

Then you get to move blocks and balloons to solve them.

It's TERRIFIC.

Give it a try by pressing this icon wherever you see it.