Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 343

• Solve linear inequalities. We solve a linear inequality in much the same way
we solve a linear equation except that we must reverse the inequality
symbol if we multiply or divide each side of the inequality by a negative
number.

• Work with double inequalities. A bounded interval is represented by a
double inequality. Figure 9-20 shows the relationship between a
bounded interval, its region on the number line, and its representation
as an interval.

Inequality Interval

a < x < b

a ≤ x ≤ b

a < x ≤ b

a ≤ x < b

Region on the Number Line

ab

ab

ab

ab

All real numbers between a and b

but not including a and b

All real numbers between a and b,

including b but not a

All real numbers between a and b,

including a but not b

All real numbers between a and b,

including a and b

(a, b)

[a, b]

(a, b]

[a, b)

FIgure 9-20

• Solve double inequalities. We solve double inequalities the same way we
solve single inequalities, except that the inequality has three quantities
instead of two “sides.” The quantity between the inequality symbols con-
tains the variable. As with other inequalities, we use addition/subtraction
and multiplication/division to isolate the variable.