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

Example 1 Ordered Pairs that Satisfy an Inequality

Example 2 Graph an Inequality

Example 3 Write and Solve an Inequality

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.

false01

true42

false20

true33

True or Falseyx

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 for in relation to the line.

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)}

Step 1 Solve for y in terms of x.Original inequalityAdd 4x to each side.

Simplify.

Divide each side by 2.

Simplify.

Step 2 GraphSince does 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

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

Answer: Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane.

Check Test 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

Answer:

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 write plus times

number of articles

she can edit is up to 8 hours.

hour

x + 8y

Step 2 Solve for y in terms of x.

Original inequality

Subtract x from each side.

Simplify.

Multiply each side by 2.

Simplify.

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:

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.

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:

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.