Problem

Use the technique described in Relating Concepts Exercises 55–58 to solve each in equality...

Use the technique described in Relating Concepts Exercises 55–58 to solve each in equality. Write each solution set in interval notation.

x2(2x − 3)2 < 0

Exercises 55

For individual or collaborative investigation

Inequalities that involve more than two factors, such as

(3x − 4)(x + 2)(x + 6) ≤ 0,

can be solved using an extension of the method shown in Examples 5 and 6. Work Exercise in order, to see how the method is extended.

Use the zero-factor property to solve (3x − 4) (x + 2) (x + 6) = 0.

Exercises 56

For individual or collaborative investigation

Inequalities that involve more than two factors, such as

(3x − 4)(x + 2)(x + 6) ≤ 0,

can be solved using an extension of the method shown in Examples 5 and 6. Work Exercise in order, to see how the method is extended.

Plot the three solutions in Exercise 55 on a number line.

Exercises 57

For individual or collaborative investigation

Inequalities that involve more than two factors, such as

(3x − 4)(x + 2)(x + 6) ≤ 0,

can be solved using an extension of the method shown in Examples 5 and 6. Work Exercise in order, to see how the method is extended.

The number line from Exercise 56 should show four intervals formed by the three points. For each interval, choose a number from the interval and decide whether it satisfies the original inequality.

Exercises 58

For individual or collaborative investigation

Inequalities that involve more than two factors, such as

(3x − 4)(x + 2)(x + 6) ≤ 0,

can be solved using an extension of the method shown in Examples 5 and 6. Work Exercise in order, to see how the method is extended.

On a single number line, graph the intervals that satisfy the inequality, including endpoints. This is the graph of the solution set of the inequality. Write the solution set in interval notation.

EXAMPLE 5

SOLVING A QUADRATIC INEQUALITY