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 – in a coordinate plane. SOLUTION STEP 1 Graph the equation of the boundary, y = – 2 x – 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 What If? Repeat the steps of Example 4 if each student group is allotted up to 420 MB of video space. STEP 1 Write an inequality. First write a verbal model. An inequality is 0.4x + 1.2y ≤ 420. SOLUTION

GUIDED PRACTICE for Examples 4 and 5 STEP 2 Graph the inequality. First graph the boundary line 0.4x + 1.2y = 420. 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.

GUIDED PRACTICE for Examples 4 and 5 STEP 3 Identify solutions. Three solutions are given below and on the graph. For the second solution, 0.4(600) + 1.2(150) = 420, so all of the available space is used. For the other two solutions, not all of the space is used. (300,200) 300 seconds of standard and 200 seconds of high quality (600, 150) 600 seconds of standard and 150 seconds of high quality (100, 300) 100 seconds of standard and 300 seconds of high quality

GUIDED PRACTICE for Examples 4 and 5 Graph the inequality in a coordinate plane. 12. y < x – STEP 1 Graph the equation of the boundary, y = x – Use a solid line because the inequality symbol is <. SOLUTION

GUIDED PRACTICE for Examples 4 and 5 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 Graph the inequality in a coordinate plane. 13. y > – x + 3 – 2 STEP 1 Graph the equation of the boundary, y = x + 3 – 2. Use a solid line because the inequality symbol is >. SOLUTION

GUIDED PRACTICE for Examples 4 and 5 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 Graph the inequality in a coordinate plane. 14. y < 3 x – 1 – 3 STEP 1 Graph the equation of the boundary, y = 3 x – 1 – 3. Use a dashed line because the inequality symbol is <. SOLUTION

GUIDED PRACTICE for Examples 4 and 5 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.