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Lesson 6 Contents Example 1Ordered Pairs that Satisfy an Inequality Example 2Graph an Inequality Example 3Write and Solve an Inequality

Example 6-1a From the set {(3, 3), (0, 2), (2, 4), (1, 0)}, which ordered pairs are part of the solution set for Use a table to substitute the x and y values of each ordered pair into the inequality. false 01 true 42 false 20 true 33 True or False yx

Example 6-1a Answer: The ordered pairs {(3, 3), (2, 4)} are part of the solution set of. In the graph, notice the location of the two ordered pairs that are solutions forin relation to the line.

Example 6-1b From the set {(0, 2), (1, 3), (4, 17), (2, 1)}, which ordered pairs are part of the solution set for Answer: {(1, 3), (2, 1)}

Example 6-2a Step 1 Solve for y in terms of x. Original inequality Add 4x to each side. Simplify. Divide each side by 2. Simplify.

Example 6-2a Step 2 Graph Sincedoes not include values when the boundary is not included in the solution set. The boundary should be drawn as a dashed line. Step 3 Select a point in one of the half-planes and test it. Let’s use (0, 0). Original inequality false y = 2x + 3

Example 6-2a Answer:Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane. y = 2x + 3

Example 6-2a Answer:Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane. CheckTest the point in the other half-plane, for example, (–3, 1). Original inequality Since the statement is true, the half-plane containing (–3, 1) should be shaded. The graph of the solution is correct. y = 2x + 3

Example 6-2b Answer:

Example 6-3a Journalism Lee Cooper writes and edits short articles for a local newspaper. It generally takes her an hour to write an article and about a half-hour to edit an article. If Lee works up to 8 hours a day, how many articles can she write and edit in one day? Step 1 Let x equal the number of articles Lee can write. Let y equal the number of articles that Lee can edit. Write an open sentence representing the situation. Number of articles she can writeplustimes number of articles she can editis up to8 hours. hour x+8y

Example 6-3a Step 2 Solve for y in terms of x. Original inequality Subtract x from each side. Simplify. Multiply each side by 2. Simplify.

Example 6-3a Step 3 Since the open sentence includes the equation, graph as a solid line. Test a point in one of the half-planes, for example, (0, 0). Shade the half-plane containing (0, 0) since is true. Answer:

Example 6-3a Step 4 Examine the situation.  Lee cannot work a negative number of hours. Therefore, the domain and range contain only nonnegative numbers.  Lee only wants to count articles that are completely written or completely edited. Thus, only points in the half-plane whose x - and y - coordinates are whole numbers are possible solutions.  One solution is (2, 3). This represents 2 written articles and 3 edited articles.

Example 6-3b Food You offer to go to the local deli and pick up sandwiches for lunch. You have $30 to spend. Chicken sandwiches cost $3.00 each and tuna sandwiches are $1.50 each. How many sandwiches can you purchase for $30? Answer:

Example 6-3b The open sentence that represents this situation is where x is the number of chicken sandwiches, and y is the number of tuna sandwiches. One solution is (4, 10). This means that you could purchase 4 chicken sandwiches and 10 tuna sandwiches.

End of Lesson 6