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Chapter 7
LINEAR INEQUALITIES
Replacing an equations equal sign with an inequality sign might, at ﬁrst
glance, seem a trivial change, but the implications are signiﬁcant. For in-
stance, whereas a linear equation in one variable has a single solution, a
typical linear inequality in one variable has inﬁnitely many solutions. The
differences are not limited to one-dimensional equations. As discussed in
Chapter 5, the graphs of linear equations are lines in the coordinate plane,
but the graphs of linear inequalities are regions of the plane.
Linear inequalities LOOK a lot like equations, but theyre very
different. The good news: Linear inequalities and linear equations act
a lot alike. If you can solve the equations in Chapter 4, and graph the
equations in Chapter 5, linear inequalities will be a piece of cake. The
bad news: Absolute value inequalities are harder than absolute value
equations.
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