LINEAR INEQUALITIES IN ONE VARIABLE, GRAPHICAL PRESENTATIONS OF SOLUTION OF LINEAR INEQUALITIES.

Subject : Mathematics

Class : JSS 2

Term : Second Term

Week : Week 5

Topic :

Polygon : Types and Angles in polygons

Previous Lesson :

Polygon : Types and Angles in a polygon

Objective:

• Students will understand what linear inequalities in one variable are and how to graphically represent them.
• Students will be able to solve problems involving linear inequalities in one variable.

Materials:

• Whiteboard and markers
• Number line posters
• Worksheets with linear inequalities word problems
• Online Resources

Content ;

LINEAR INEQUALITIES IN ONE VARIABLE, GRAPHICAL PRESENTATIONS OF SOLUTION OF LINEAR INEQUALITIES.

Linear inequalities in one variable are mathematical expressions that compare two values using the symbols <, >, ≤ or ≥. The variable is usually represented by a letter such as x, and the inequality describes the relationship between x and another number or expression.

For example, the inequality 2x + 3 < 7 means that when you plug in a value for x, multiply it by 2, add 3, and compare the result to 7, the expression on the left side is less than the expression on the right side.

Graphical presentations of solutions of linear inequalities involve plotting the inequality on a number line to show which values of x satisfy the inequality. To do this, we mark the numbers that make the inequality true and draw a shaded region on the number line to indicate the possible values of x.

For example, let’s graph the inequality 2x + 3 < 7 on a number line. To start, we isolate x by subtracting 3 from both sides: 2x < 4. Then, we divide both sides by 2 to get x < 2. This means that any value of x less than 2 makes the inequality true.

To graph this on a number line, we put a dot at 2 and draw an arrow to the left to show that all values less than 2 satisfy the inequality. We shade the region to the left of the dot to show this visually.

Another example is the inequality 5x – 4 > 11. To solve for x, we add 4 to both sides: 5x > 15. Then, we divide both sides by 5 to get x > 3. This means that any value of x greater than 3 makes the inequality true.

To graph this on a number line, we put a dot at 3 and draw an arrow to the right to show that all values greater than 3 satisfy the inequality. We shade the region to the right of the dot to show this visually.

By graphing linear inequalities on a number line, we can visualize the range of values that satisfy the inequality and better understand the relationships between variables

Evaluation

1. Which symbol is used to represent “less than or equal to” in linear inequalities? a) < b) > c) ≤ d) ≥
2. What is the solution set for the inequality x + 2 > 5? a) x > 3 b) x < 3 c) x ≥ 3 d) x ≤ 3
3. Which of the following inequalities is represented by a shaded region to the right of a dot on a number line? a) x < 2 b) x > -1 c) x ≤ 5 d) x ≥ 7
4. What is the solution set for the inequality 2x – 3 ≤ 9? a) x ≤ 6 b) x ≥ 6 c) x < 6 d) x > 6
5. Which of the following inequalities has a solution set that includes the number 4? a) 3x – 5 > 7 b) 2x + 1 < 9 c) 5 – x ≥ 2 d) x + 4 ≤ 10
6. What is the solution set for the inequality 4x + 2 > 10? a) x > 2 b) x < 2 c) x ≥ 2 d) x ≤ 2
7. Which of the following inequalities is represented by a shaded region to the left of a dot on a number line? a) x > -3 b) x < 0 c) x ≥ 2 d) x ≤ -5
8. What is the solution set for the inequality 7x – 3 < 10x + 2? a) x < 1/3 b) x > 1/3 c) x ≤ 1/3 d) x ≥ 1/3
9. Which of the following inequalities is true for all values of x? a) 2x + 5 > 2x – 3 b) 3x + 4 < 4x – 1 c) x – 2 ≤ x + 2 d) 5x + 3 ≥ 3x – 5
10. Which of the following inequalities has a solution set that includes all real numbers? a) 3x + 2 > 0 b) 2x – 5 < 7 c) 4 – x ≤ 6 d) x + 1 ≥ -1

Lesson Presentation

Revision of last lesson 

• Polygon : Types and Angles in a polygon

Introduction (10 minutes):

1. Ask students if they know what an inequality is and give a few examples (e.g. 2 < 5, 6 > 3, etc.).
2. Explain that a linear inequality in one variable is an inequality that involves only one variable, such as x.
3. Define the symbols used in linear inequalities (<, >, ≤, ≥) and give examples of each.
4. Show a number line poster and explain how it can be used to represent the solutions to linear inequalities.

Lesson (30 minutes):

1. Give students a worksheet with linear inequalities word problems and ask them to solve the problems by setting up and graphing linear inequalities on a number line.
2. Walk students through the steps of graphing a linear inequality on a number line. For example, if the inequality is x + 2 < 5, start by subtracting 2 from both sides to get x < 3. Then, plot a dot at 3 and draw an arrow to the left to represent all values less than 3 that satisfy the inequality.
3. Have students practice graphing linear inequalities on a number line by working through a few examples together as a class.
4. Review the concept of shading the region on the number line that represents the possible solutions to the inequality.

Conclusion (10 minutes):

1. Review the key concepts of linear inequalities in one variable and graphical representations of solutions to linear inequalities.
2. Ask students if they have any questions or if they would like to practice more examples.
3. Encourage students to use number lines when solving linear inequalities in the future.

Assessment:

• Observe students as they work on the worksheet and provide feedback.
• Have students present their solutions to the class and explain their reasoning.
• Ask students to create their own word problems involving linear inequalities in one variable and have them solve the problems and graph the solutions

Weekly Assessment /Test

1. A linear inequality is an inequality that involves only ____________.
2. The symbols used in linear inequalities are <, >, ≤, and ____________.
3. To solve a linear inequality, we must isolate the variable on one side of the inequality sign and use ____________ to represent the solutions.
4. The graphical presentation of a solution to a linear inequality is done on a ____________.
5. When graphing a linear inequality on a number line, we put a dot at the solution and draw an arrow to the ____________.
6. The shaded region on a number line represents the ____________ values that satisfy the inequality.
7. The inequality x + 4 < 10 can be rewritten as x < ____________.
8. The inequality 5x – 2 ≥ 8 can be rewritten as x ____________ 2.
9. The inequality 3x + 2 ≤ 11 can be rewritten as x ____________ 3.
10. The inequality -2x + 5 > 1 can be rewritten as x < ____________.