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Solve a multi-step problem

EXAMPLE 4. Solve a multi-step problem. Movie Recording.

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Solve a multi-step problem

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  1. EXAMPLE 4 Solve a multi-step problem Movie Recording 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.

  2. 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.

  3. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP1 Write an inequality. First write a verbal model. An inequality is 0.4x +1.2y ≤ 300.

  4. EXAMPLE 4 Solve a multi-step problem STEP2 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 xand ycannot be negative, shade only points in the first quadrant.

  5. (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 EXAMPLE 4 Solve a multi-step problem STEP3 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.

  6. Graph y> – 2 x – 3 + 4 in a coordinate plane. Graph the equation of the boundary, y =–2 x – 3 + 4. Use a dashed line because the inequality symbol is > . EXAMPLE 5 Graph an absolute value inequality SOLUTION STEP1 STEP2 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.

  7. for Examples 4 and 5 GUIDED PRACTICE What If?Repeat the steps of Example 4 if each student group is allotted up to 420 MB of video space. ANSWER STEP3 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

  8. y<x – 2 + 1 for Examples 4 and 5 GUIDED PRACTICE Graph the inequality in a coordinate plane. ANSWER

  9. y>–x + 3 – 2 for Examples 4 and 5 GUIDED PRACTICE Graph the inequality in a coordinate plane. ANSWER

  10. y<3x – 1 – 3 for Examples 4 and 5 GUIDED PRACTICE Graph the inequality in a coordinate plane. ANSWER

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