Chapter 2

Section 8

Standardized Test Practice

EXAMPLE 1

SOLUTION

Ordered pair Substitute Conclusion

(6, –3) (6, –3) is not a solution

(0, 2) is not a solution(0, 2)

(–2 , –1) is not a solution(–2, –1)

(–3, 5) is a solution3(–3) + 4(5) = 11 > 8(–3, 5)

3(–2) + 4(–1) = –10 > 8

3(6) + 4(– 3) = 6 > 8

3(0) + 4(2) = 8 > 8

Standardized Test Practice

EXAMPLE 1

ANSWER

The correct answer is D.

GUIDED PRACTICE for Example 1

Tell whether the given ordered pair is a solution of 5x – 2y ≤ 6.

Ordered pair Conclusion

1. (0, –4) (0, – 4 ) is not a solution

2. (2, 2) (2, 2 ) is a solution

3. (–3, 8) (–3, 8 ) is a solution

4. (–1, –7) (– 1, – 7 ) is not a solution

ANSWER

Graph linear inequalities with one variable

EXAMPLE 2

Graph (a) y < –3 and (b) x < 2 in a coordinate plane.

Test the point (0,0). Because (0,0) is not a solution of the inequality, shade the half- plane that does not contain (0,0).

a. Graph the boundary line y = –3. Use a solid line because the inequality symbol is < .

Graph linear inequalities with one variable

EXAMPLE 2

b. Graph the boundary line x = 2.Use a dashed line because the inequality symbol is < .

Test the point (0,0). Because (0,0) is a solution of the inequality, shade the half-plane that does not contains (0,0).

Graph linear inequalities with two variables

EXAMPLE 3

Graph (a) y > –2x and (b) 5x – 2y ≤ –4 in a coordinate plane.

a. Graph the boundary line y = –2x. Use a dashed line because the inequality symbol is >.

Test the point (1,1). Because (1,1) is a solution of the inequality, shade the half-plane that contains (1,1).

Graph linear inequalities with two variables

EXAMPLE 3

Test the point (0,0). Because (0,0) is not a solution of the inequality, shade the half-plane that does not contain (0,0).

b. Graph the boundary line 5x –2y = –4.Use a solid line because the inequality symbol is < .

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

5. y > –1

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

6. x > –4

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

7. y > –3x

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

8. y < 2x +3

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

9. x + 3y < 9

GUIDED PRACTICE for Examples 2 and 3

Graph the inequality in a coordinate plane.

10. 2x – 6y > 9

Solve a multi-step problem

EXAMPLE 4

A film class is recording a DVD of student-made short films. Each student group is allotted up to 300 megabytes (MB) of video space. The films are encoded on the DVD at two different rates: a standard rate of 0.4 MB/sec for normal scenes and a high-quality rate of 1.2 MB/sec for complex scenes.

Movie Recording

EXAMPLE 4 Solve a multi-step problem

• Write an inequality describing the possible amounts of time available for standard and high-quality video.

• Graph the inequality.

• Identify three possible solutions of the inequality.

EXAMPLE 4

STEP 1

Write an inequality. First write a verbal model.

An inequality is 0.4x + 1.2y ≤ 300.

SOLUTION

Solve a multi-step problem

EXAMPLE 4

Graph the inequality. First graph the boundary line 0.4x + 1.2y = 300. Use a solid line because the inequality symbol is ≤ .

Test the point (0, 0). Because (0, 0) is a solution of the inequality, shade the half-plane that contains (0, 0). Because x and y cannot be negative, shade only points in the first quadrant.

Solve a multi-step problem

STEP 2

EXAMPLE 4

STEP 3

Identify solutions. Three solutions are given below and on the graph.

For the first solution, 0.4(150) + 1.2(200) = 300, so all of the available space is used. For the other two solutions, not all of the space is used.

Solve a multi-step problem

(150, 200) 150 seconds of standard and 200 seconds of high quality

(300, 120) 300 seconds of standard and 120 seconds of high quality

(600, 25) 600 seconds of standard and 25 seconds of high quality

Graph an absolute value inequality

EXAMPLE 5

Graph y > – 2 x – 3 + 4 in a coordinate plane.

SOLUTION

STEP 1

Graph the equation of the boundary, y = –2 x – 3 + 4. Use a dashed line because the inequality symbol is > .

STEP 2

Test the point (0, 0). Because (0, 0) is a solution of the inequality, shade the portion of the coordinate plane outside the absolute value graph.

GUIDED PRACTICE for Examples 4 and 5

11. What If? Repeat the steps of Example 4 if each student group is allotted up to 420 MB of video space.

STEP 3

300 seconds of standard 200 seconds of high quality, 600 seconds of standard 150 seconds of high quality, or 100, seconds of standard 300 seconds of high quality

ANSWER

GUIDED PRACTICE for Examples 4 and 5

Graph the inequality in a coordinate plane.

12. y < x – 2 + 1

ANSWER

GUIDED PRACTICE for Examples 4 and 5

Graph the inequality in a coordinate plane.

13. y > – x + 3 – 2

ANSWER

GUIDED PRACTICE for Examples 4 and 5

Graph the inequality in a coordinate plane.

14. y < 3 x – 1 – 3

ANSWER