Graphical Solutions of a “Less Than”Linear Inequality in One Variable

To determine the solutions of the inequality , graph the functions and . Sketch the graphs. Label the points of intersection of the graphs.

2 3 5 x xY1 2 3 x Y2 5 x

1. The intersection of the two graphs is _____.2. The solution that corresponds to the equality is _____.

Choose the correct answer.

3. To solve a “less than” inequality, Y1 < Y2, locate the portion of the Y1graphabove/below the Y2 graph. When tracing the graph of Y1, you will find that this is to the left/right of the intersection. The x-coordinate of the points in this direction are less than/greater than the x-coordinate of the point of intersection. 4. Combining the solutions found for the equality and the “less than,” we determine that the solution set is _____.

Chapter 7Discovery 1

Graphical Solutions of a “Greater Than”Linear Inequality in One Variable

To determine the solutions of the inequality , graph the functions and . Sketch the graphs. Label the points of intersection of the graphs.

2 3 5 x xY1 2 3 x Y2 5 x

1. The intersection of the two graphs is _____.2. The solution that corresponds to the equality is _____.

Choose the correct answer.

3. To solve a “greater than” inequality, Y1 > Y2, locate the portion of the Y1graphabove/below the Y2 graph. When tracing the graph of Y1, you will find that this is to the left/right of the intersection. The x-coordinate of the points in this direction are less than/greater than the x-coordinate of the point of intersection. 4. Combining the solutions found for the equality and the “greater than,” we determine that the solution set is _____.

Chapter 7Discovery 2

Addition Property of Inequalities

1. Given the inequality 10 < 12, add 2 to both expressions and check whether the new expression is also true.

10 < 1210 + 2 12 + 2

12 14

2. Given the inequality 10 < 12, add -2 to both expressions and checkwhether the new expression is also true.3. Given the inequality 10 < 12, subtract 2 from both expressions and check whether the new expression is also true.4. Given the inequality 10 < 12, subtract -2 from both expressions and check whether the new expression is also true.

Write a rule for the addition property of inequalities.

True

Chapter 7Discovery 3

Multiplication Property of Inequalities

1. Given the inequality 10 < 12, multiply both expressions by 2 and check whether the new expression is also true.

10 < 1210 • 2 12 • 2

20 24 True

2. Given the inequality 10 < 12, multiply both expressions by -2 and check whether the new expression is also true.3. Given the inequality 10 < 12, divide both expressions by 2 and check whether the new expression is also true.4. Given the inequality 10 < 12, divide both expressions by -2 and check whether the new expression is also true.

Write a rule for the multiplication property of inequalities.

Chapter 7Discovery 4

Graphing a “Less Than or Equal To”Linear Inequality in Two Variables

Graph the line determined by the equation

1. Use Trace to determine the coordinates of points on the line.a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

2. Clear the trace, and use the free-moving cursor (arrow keys) to determine ordered pairs above the line.

a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

3. Now use the free-moving cursor (arrow keys) to determine orderedpairs below the line.

a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

Chapter 7Discovery 5

Write a rule for graphing a “less than or equal to” linear inequality.

2 4? y x

2 4? y x

2 4? y x

2 4. y x

Graphing a “Greater Than”Linear Inequality in Two Variables

Graph the line determined by the equation

1. Use Trace to determine the coordinates of points on the line.a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

2. Clear the trace, and use the free-moving cursor (arrow keys) to determine ordered pairs above the line.

a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

3. Now use the free-moving cursor (arrow keys) to determine orderedpairs below the line.

a. List two of these ordered pairs.b. Are the ordered pairs solutions of the inequality

Chapter 7Discovery 6

Write a rule for graphing a “greater than” linear inequality.

2 4. y x

2 4? y x

2 4? y x

2 4? y x