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The Humongous Book of Algebra Problems by W. Michael Kelley

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Chapter 4
LINEAR EQUATIONS IN ONE VARIABLE
This chapter explores basic linear equationsequations with degree one—
that are expressed in terms of a single, unique variable. Unlike the expres-
sions of Chapter 3, equations are complete algebraic sentences, statements
that express the equality of two expressions that are separated by an equal
sign.
The difference between an expression and an equation can be
expressed in two words: equal sign. Expressions dont have them but
equations do. That one little symbol makes a huge difference. For
one thing, your overall goal is different. You spent most of Chapter 3
simplifying equations, writing the same expression in a different, usually
shorter, way. Equations are easier to deal with than expressions,
because you actually get a tangible numeric answer, one that you
can go back and check to make sure you got it right.
In this chapter, you start out with basic equation–solving techniques,
and they’ll slowly evolve, becoming more and more complicated. By
the end, you should be able to solve just about any equation they
throw at you, if theres only one unique variable is in the equation
(like x) and that variable is only raised to the rst power.
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