Balance as a model of an equationThis article discusses how to use the balance as a model or illustration of simple equations for students who are just starting to study equations. An equation is basically saying that two things are EQUAL. Since in a balanced situation the two sides of the balance hold equal weight, we can model simple equations with a balance. In the pictures balls represent ones, and the block represents the unknown x. To find out what the block weighs, you can
That way you will maintain the balance (or the equality in the equation).
DividingIn some situations you have to divide both sides of the equation by the same number. When is that? It's basically when you have the happy situation where there are ONLY x's (blocks) on one side but there's more than one.
Combining the operationsThe legal operations thus are:
(There are others too but those are not needed in these simple equations.) The goal is to
FIRST add and subtract until we arrive to a situation where on one
side there are ONLY x's (blocks) and on the other side there are ONLY ones (balls).
Example of both subtracting and dividingIn this example we use all the abovementioned operations: taking away from both sides of the equation and dividing the equation by the same number.
Try substituting this value x = 1 1/2 into the original equation 4x + 2 = 2x + 5 and check if the equation becomes true! These equations are simple enough that you can solve them using this balance model. ALWAYS check your solution by substituting to the original equation.
Continue to Negative terms in an equation How to teach equation solving: example (from my blog)
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