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Introduction to One-Variable Inequalities – Recap: Inequalities vs Equations – Inequalities show a relationship of less than/greater than, unlike equations’ exact equality. – Decipher inequality symbols – Symbols: (greater than), d (less than or equal), e (greater than or equal). – Real-life inequality examples – Budgeting allowance, temperature ranges, or height restrictions for rides. – Solving with variables on both sides – Combine like terms and isolate the variable to find the solution set. | Begin with a brief review of inequalities, emphasizing how they represent a range of possible solutions, in contrast to the single solution of an equation. Explain the meaning of each inequality symbol and how to read them. Provide relatable examples that students might encounter in their daily lives, such as budgeting their allowance or understanding height requirements for amusement park rides. Finally, introduce the concept of solving inequalities that have variables on both sides, stressing the importance of maintaining the inequality’s direction while isolating the variable. This will set the foundation for more complex problem-solving involving inequalities.

Solving Simple Inequalities – Review solving one-variable inequalities – Recall steps: isolate variable, use inverse operations – Practice problem: 3x > 9 – Find x by dividing both sides by 3: x > 3 – Maintain inequality balance – When multiplying/dividing by a negative, flip the inequality sign – Understand inequality solutions – Solutions represent a range of values, not just one number | Begin with a quick review of the steps to solve simple inequalities, emphasizing the use of inverse operations to isolate the variable. Present the practice problem 3x > 9 and solve it together, demonstrating that dividing both sides by 3 yields the solution x > 3. Highlight the importance of maintaining the inequality balance throughout the process, especially when multiplying or dividing by a negative number, which requires flipping the inequality sign. Conclude by discussing that solutions to inequalities represent a range of values, which can be graphed on a number line. Encourage students to practice with additional problems to reinforce their understanding.

Solving Inequalities: Variables on Both Sides – Inequalities with variables on both sides – Goal: Isolate the variable – Move all variables to one side of the inequality – Example: 2x + 3 d 5x – 2 – Subtract 2x from both sides: 3 d 3x – 2 – Steps to solve the inequality – Add 2, divide by 3: x d 5/3 | This slide introduces students to solving inequalities that have variables on both sides. The objective is to isolate the variable on one side to find the solution set. Start with an example like 2x + 3 d 5x – 2 and demonstrate the steps to solve it: subtract 2x from both sides to get 3 d 3x – 2, then add 2 to both sides to get 5 d 3x, and finally divide by 3 to isolate x, resulting in x d 5/3. Emphasize the importance of maintaining the balance of the inequality throughout the process. Encourage students to practice with additional examples and to check their solutions by substituting values back into the original inequality.

Solving Inequalities: Variables on Both Sides – Simplify both sides first – Combine like terms and remove parentheses – Move variables to one side – Use addition or subtraction to get variables on one side – Isolate the variable to solve – Use multiplication or division to get the variable alone – Check solution with original inequality – Substitute the solution back to ensure it works | This slide outlines the steps to solve inequalities with variables on both sides, which is a key concept in understanding one-variable inequalities. Start by simplifying both sides of the inequality by combining like terms and removing any parentheses. Next, move all variables to one side of the inequality using addition or subtraction. Then, isolate the variable by using multiplication or division to solve for the variable. Lastly, always check the solution by substituting it back into the original inequality to ensure it makes the inequality true. Provide examples for each step to ensure students can follow along and understand the process. Encourage students to practice these steps with different inequalities to gain confidence in solving them.

Solving Inequalities with Variables on Both Sides – Flip inequality for negative coefficients – When you multiply/divide by a negative, reverse the inequality sign. – Substitute to verify solutions – After finding a solution, plug it back into the original to check. – Solve 4x – 5 < 3 – 2x – Combine like terms and isolate x to find the solution. – Practice with similar problems | This slide focuses on key strategies for solving one-variable inequalities, especially when variables appear on both sides of the inequality. Emphasize the importance of reversing the inequality sign when multiplying or dividing by a negative number, as this is a common mistake. Encourage students to always check their solutions by substituting them back into the original inequality to ensure accuracy. Use the provided practice problem to demonstrate these concepts step by step, and then assign similar problems for students to solve independently, reinforcing the learning objectives.

Avoiding Common Mistakes: Inequalities – Remember to flip inequality when multiplying/dividing by a negative – If you multiply or divide both sides by a negative, the inequality direction changes. – Distribute negative signs correctly – Ensure every term inside parentheses is affected by the negative sign. – Example: Correcting a common error – Incorrect: -3(x + 4) > 12 becomes -3x + 12 > 12. Correct: -3(x + 4) > 12 becomes -3x – 12 > 12. | When teaching inequalities, it’s crucial to emphasize the importance of maintaining the balance of the equation while following the rules. A common error is forgetting to flip the inequality sign when multiplying or dividing by a negative number. This can lead to the wrong solution set. Another frequent mistake is not properly distributing negative signs, especially when they are outside parentheses. Provide an example on the board, showing both the incorrect and correct methods. Walk through the steps to solve the inequality, highlighting where the mistakes typically occur and how to avoid them. Encourage students to double-check their work for these errors.

Solving Inequalities: Practice Problems – Solve 5x + 7 e 2x + 16 – Subtract 2x from both sides, then subtract 7. – Solve -3x – 4 < 6 – x – Add 3x to both sides, then add 4. – Solve 7 – 2y d 3y + 8 – Add 2y to both sides, then subtract 8. | This slide presents practice problems for students to apply their understanding of solving one-variable inequalities with variables on both sides. For each inequality, students should perform inverse operations to isolate the variable on one side of the inequality. Remind them to reverse the inequality sign when multiplying or dividing by a negative number. Provide guidance on the steps for solving each problem and encourage students to check their solutions by substitizing the values back into the original inequalities. Possible activities include working in pairs to solve the inequalities, creating a step-by-step guide for solving one-variable inequalities, or having students come up to the board to solve the problems and explain their reasoning.

Class Activity: Inequality Challenge – Work in pairs on inequalities – Each pair solves and presents one – Present your solution and explain your reasoning – Discuss various solving methods – Compare different strategies used by classmates – Explore different solutions | This activity is designed to foster collaborative problem-solving skills among students while deepening their understanding of solving inequalities with variables on both sides. Students should be encouraged to discuss their thought processes and the steps they took to arrive at their solutions. As they present, highlight the importance of checking their work by substituting the solution back into the original inequality. Provide guidance on different methods such as the balance method, where both sides of the inequality are kept balanced while isolating the variable. Offer at least four different inequalities of varying difficulty to cater to different skill levels within the class. This will ensure that all students are challenged appropriately and can contribute meaningfully to the class discussion.

Wrapping Up: Inequalities with Variables on Both Sides – Review of solving inequalities – Homework: 10 practice problems – Solve inequalities with variables on each side and check your solutions. – Encourage regular practice – Practice makes perfect! Try to solve them without peeking at the answers. – Bring questions to next class – Don’t hesitate to ask if you’re unsure about any steps! | As we conclude today’s lesson on solving inequalities with variables on both sides, remind students of the key strategies discussed: isolating the variable, using inverse operations, and checking solutions by substituting back into the original inequality. For homework, students are assigned 10 problems to reinforce these concepts. Encourage them to practice independently and come prepared with questions for the next class. This will help solidify their understanding and address any uncertainties they may have encountered during their practice.