Chapter 7

LINEAR INEQUALITIES

Replacing an equation’s 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 they’re 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.

T

h

e

y

’r

e

l

i

k

e

e

q

u

a

t

i

o

n

s

w

i

t

h

o

u

t

t

h

e

e

q

u

a

l

s

i

g

n

Start Free Trial

No credit card required