Intermediate Algebra (11th edition)

Now try 0 from Interval B.

Original inequality

Let

False

The numbers in Interval B are notsolutions. Verify that the test number 5 from Inter-

val C satisfies the inequality, so all numbers there are also solutions.

Based on these results (shown by the colored letters in FIGURE 19), the solution set

includes the numbers in Intervals A and C, as shown on the graph in FIGURE 20. The

solution set is written in interval notation as

1 - q, - 32 ́ 1 4, q 2.

- 1270

02 - 0 - 127 x=0.

?

0

x^2 - x- 1270

554 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

NOW TRY
EXERCISE 2
Solve and graph the solution
set.

x^2 + 2 x- 870

–3 04

FIGURE 20

NOW TRY
EXERCISE 3
Solve each inequality.

(a)

(b) 14 x- 122 6- 3

14 x- 122 7- 3

Solving Special Cases

Solve each inequality.

(a)

Because is never negative, it is always greater than Thus, the

solution set for is the set of all real numbers,

(b)

Using the same reasoning as in part (a), there is no solution for this inequality.

The solution set is 0.

12 x- 322 6- 1

12 x- 322 7- 1 1 - q, q 2.

12 x- 322 - 1.

12 x- 322 7- 1

EXAMPLE 3

Solving a Quadratic Inequality

Step 1 Write the inequality as an equation and solve it.

Step 2 Use the solutions from Step 1 to determine intervals.Graph the

numbers found in Step 1 on a number line. These numbers divide

the number line into intervals.

Step 3 Find the intervals that satisfy the inequality. Substitute a test

number from each interval into the original inequality to determine

the intervals that satisfy the inequality. All numbers in those intervals

are in the solution set. A graph of the solution set will usually look

like one of these. (Square brackets might be used instead of paren-

theses.)

or

Step 4 Consider the endpoints separately.The numbers from Step 1 are

included in the solution set if the inequality symbol is or. They

are not included if it is 6 or 7.

... Ú

This agrees with the solution set found in Example 1(a). NOW TRY

In summary, follow these steps to solve a quadratic inequality.

NOW TRY

NOW TRY ANSWERS
2.

3. (a) 1 - q, q 2 (b) 0

1 - q, - 42 ́ 1 2, q 2

–4 0 2