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Introduction to Inequalities – Define inequalities – An inequality shows the relationship between two expressions that are not equal. – Inequalities vs. equations – Unlike equations, inequalities do not show equality but a range of possible solutions. – Inequalities in daily life – Budgeting allowance, or minimum height for a ride. – Solving inequality basics | This slide introduces the concept of inequalities, which are statements that describe a range of possible solutions, unlike equations that pinpoint a single solution. Start by defining inequalities and comparing them to equations to highlight the differences. Use relatable real-life examples, such as budgeting a weekly allowance or the minimum height requirement for an amusement park ride, to illustrate how inequalities are present in everyday situations. Explain that solving inequalities involves finding all possible values that make the inequality true, which is a fundamental skill in algebra. Encourage students to think of other examples where they encounter inequalities in their daily lives.

Types of Inequalities – Understanding ‘>’ and ” means more than, ‘<' means less than. – Interpreting 'e' and 'd' – 'e' includes the number, 'd' means up to and including. – Meaning of '`' – '`' indicates that values are not the same. – Applying inequalities in problems | This slide introduces students to the basic types of inequalities they will encounter in algebra. Start by explaining the symbols for ‘greater than’ (>) and ‘less than’ (<), which compare two values. Then, discuss 'greater than or equal to' (e) and 'less than or equal to' (d), emphasizing that these inequalities include the number itself. Introduce 'not equal to' (`) as a way to represent values that are not the same. Use number lines and simple examples to illustrate each type. Encourage students to think of real-life situations where these inequalities apply, such as minimum age requirements or maximum capacity limits. This foundational knowledge will be crucial for solving and graphing one-variable inequalities.

Solving Simple Inequalities – Isolate the variable on one side – Move all variables to one side of the inequality – Use addition or subtraction to solve – Adjust the inequality by adding or subtracting terms – Check the solution – Substitute the solution back to verify – Understand inequality solutions – Solutions can be a range of values, not just one number | This slide introduces students to the process of solving simple one-variable inequalities. Start by explaining the importance of getting the variable alone on one side of the inequality, which often involves moving terms from one side to the other. Emphasize the use of addition or subtraction to balance the inequality, and remind students that whatever operation is done to one side must be done to the other. Stress the importance of checking their work by substituting the solution back into the original inequality to ensure it makes a true statement. Finally, discuss how solutions to inequalities can represent a range of values, and contrast this with solutions to equations that typically have a single value. Provide examples and encourage students to practice with problems of varying difficulty.

Solving Inequalities and Graphing – Understanding inequality solutions – Solutions are values that make the inequality true. – How to graph on a number line – Plot solutions as shaded regions on the line. – Example: x > 5 – For x > 5, shade right from 6, not including 5. | This slide introduces students to the concept of solutions to inequalities and how to represent them graphically. Begin by explaining that a solution to an inequality is any value that makes the inequality true. Then, demonstrate how to graph these solutions on a number line, emphasizing the difference between ‘greater than’ and ‘less than’ and how to show this with open or closed circles and shading. Use the example ‘x > 5’ to show that all numbers greater than 5 are solutions, and illustrate this on the number line by shading to the right of the point 5, which remains unshaded (open circle) to indicate that it is not included in the solution set. Encourage students to practice with additional examples.

Solving Complex Inequalities – Solve using multiplication/division – Flip sign when using negative numbers – If you multiply/divide by a negative, the inequality direction changes – Example: -2x d 8 – Dividing by -2, we get x e -4 – Practice with different inequalities – Try solving x > -6 after multiplying by -3 | This slide introduces students to solving inequalities involving multiplication or division. Emphasize the critical rule that when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign must be flipped. Use the example -2x d 8 to demonstrate this concept. Divide both sides by -2, remembering to flip the inequality sign, resulting in x e -4. Encourage students to practice this technique with various inequalities, reinforcing the rule about flipping the sign. Provide additional practice problems where students can apply this rule and verify their solutions.

Compound Inequalities: ‘And’ & ‘Or’ – ‘And’ vs. ‘Or’ inequalities – ‘And’ means both conditions must be true; ‘Or’ means either can be true. – How to graph on a number line – Plot the solutions for ‘x’ that make the inequality true. – Example: 3 -2 and x d 3. – Practice with different examples | This slide introduces compound inequalities, focusing on the concepts of ‘And’ and ‘Or’ inequalities. ‘And’ inequalities require both conditions to be met simultaneously, while ‘Or’ inequalities are satisfied if either condition is met. Students will learn to graph these inequalities on a number line, visualizing the range of solutions. The example 3 < x + 5 d 8 will be solved step by step, demonstrating how to find the value of 'x' that satisfies the inequality and how to represent it graphically. Encourage students to practice with different examples to solidify their understanding. Provide additional practice problems for students to solve and graph as homework.

Solving Inequality Word Problems – Translate words into inequalities – Convert verbal statements into mathematical expressions – Solve and graph inequalities – Find the solution set and represent it on a number line – Discuss an example problem – ‘At least 15 candies to win a prize’ means you need 15 or more candies – Practice with class activities | This slide aims to teach students how to approach word problems that involve inequalities. Start by translating the verbal statements into mathematical expressions, ensuring students understand keywords like ‘at least’, ‘no more than’, etc. Then, demonstrate how to solve the inequalities and represent the solution set on a number line. Use an example such as a carnival game where you need at least 15 candies to win a prize to illustrate how to set up and solve an inequality. Finally, engage the class with practice problems where they can apply these skills and discuss their solutions.

Class Activity: Inequality Challenge – Pair up and solve inequalities – Graph solutions on a number line – Mark the solution set clearly on the line – Present solutions to the class – Explain your reasoning – Discuss how you determined the solution set | This activity is designed to promote collaborative problem-solving and to reinforce the concept of inequalities. Students should work in pairs to solve a set of inequality problems, which encourages peer learning. Once they’ve found the solutions, they should graph them on a number line, which helps visualize the concept. After graphing, each pair will present their solutions to the class, explaining the steps they took to solve the inequalities and how they determined the solution set. This will help students articulate their thought process and solidify their understanding. For the teacher: Prepare a diverse set of inequality problems of varying difficulty. Ensure students understand how to graph inequalities and provide guidance as needed. Encourage students to ask questions during presentations to engage with the material actively.