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By example, the additive principle is explained.

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Equivalent Equations

The basic approach to finding the solution to equations is to change the equation into simpler equations, but in such a way that the solution set of the new equation is the same as the solution set of the original equation. When two equations have the same solution set, we say that they are equivalent.

What we want to do when we solve an equation is to produce an equivalent equation that tells us the solution directly. For example, let's look at the equation

2x + 3 = 7,

we can say that the equation

x = 2

is an equivalent equation, because they both have the same solution, namely x = 2.

We need to have some way to convert an equation like 2x + 3 = 7 into an equivalent equation like x = 2 that tells us the solution. We solve equations by using ...

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