Practice - Chapter 4: Solving Linear Inequalities
Practice Questions
Test your understanding with targeted questions
Solve the one-step inequality: x - 8 < 15.
* Answer: x < 23.
* Hint: Use the inverse operation of subtraction to isolate the variable x.
💡 Hint: Use the inverse operation of subtraction to isolate the variable x.
What type of circle (open or closed) is used to graph the solution for the inequality y >= -4?
* Answer: Closed circle ( • ).
* Hint: The symbol includes the "equal to" component, meaning the value itself is part of the solution set.
💡 Hint: The symbol includes the "equal to" component, meaning the value itself is part of the solution set.
7 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
When solving -4x < 24, what is the result, including the correct inequality sign?
* Type: mcq
* Options: x < -6, x <= -6, x > -6
* Correct Answer: x > -6
* Explanation: The inequality sign must be reversed when dividing both sides by the negative number, -4.
* Hint: This question tests the crucial exception rule for solving inequalities.
💡 Hint: This question tests the crucial exception rule for solving inequalities.
True or False: The solution to x + 1 >= 5 is represented by a closed circle on the number line.
* Type: boolean
* Options: True, False
* Correct Answer: True
* Explanation: The >= symbol includes the value, requiring a closed circle ( • ) to show that the boundary point is part of the solution set.
* Hint: Look closely at the inequality symbol to see if it includes "or equal to."
💡 Hint: Look closely at the inequality symbol to see if it includes "or equal to."
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Applying Mathematics (D): A student has a budget of $150 for new art supplies. She wants to buy a sketchbook for $25 and use the rest of the money to buy pencils that cost $15 per set.
* Task: Write an inequality to model this situation and solve it to find the maximum number of pencil sets (p) she can buy.
* Solution:
* Inequality: 15p + 25 <= 150
* Solving:
1. Subtract 25 from both sides: 15p <= 125
2. Divide both sides by 15: p <= 8.333...
* Conclusion: Since she can only buy whole sets, the maximum number of pencil sets she can buy is 8.
* Hint: The word "budget" means her total spending must be less than or equal to a certain amount.
💡 Hint: The word "budget" means her total spending must be less than or equal to a certain amount.
Investigating Patterns (B) & Communication (C): Two different gyms offer membership plans.
* Gym A: $50 sign-up fee plus $20 per month.
* Gym B: No sign-up fee, but $30 per month.
* Task: Write and solve an inequality to determine after how many months (m) the total cost of Gym A will be less than the total cost of Gym B. Clearly state the solution set.
* Solution:
* Cost A: 50 + 20m
* Cost B: 30m
* Inequality (Cost A < Cost B): 50 + 20m < 30m
* Solving:
1. Subtract 20m from both sides: 50 < 10m
2. Divide by 10: 5 < m or m > 5
* Conclusion (Solution Set): The cost of Gym A is less than Gym B starting at month 6 (after 5 months have passed). The solution set is all whole numbers greater than 5.
* Hint: Set up expressions for the total cost of each gym and compare them using the "less than" symbol.
💡 Hint: Set up expressions for the total cost of each gym and compare them using the "less than" symbol.
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