Mathematics
Grade 9
15 min
Identify solutions to inequalities
Identify solutions to inequalities
What you'll learn
- Identify whether one group of objects has more, less, or the same number of objects as another group by counting.
- Explain, using drawings or manipulatives, why one event is more likely, less likely, or equally likely to occur compared to another.
- Solve simple problems by comparing the number of objects in two groups to determine which group has more, less, or the same.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define what a solution to an inequality is.
Test a given numerical value to determine if it is a solution to a linear inequality.
Test a given numerical value to determine if it is a solution to a simple quadratic inequality.
Differentiate between strict inequalities (<, >) and non-strict inequalities (≤, ≥) when testing boundary points.
Explain the difference between a single solution and a solution set.
Verify solutions involving integers, fractions, and negative numbers.
Ever tried to fit your luggage into an airline's overhead bin? You're checking if its size is less than or equal to the maximum allowed—that's identifying a solution to an inequality! ✈️
This tutorial will teach you the fundamental skill of testing numbers to see...
2
Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two expressions using an inequality symbol. It shows that the two sides are not necessarily equal.3x - 5 > 10 is an inequality. Other symbols include < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).
SolutionA value for a variable that makes an inequality a true statement.For the inequality x + 2 > 5, the number x = 4 is a solution because 4 + 2 > 5 (which simplifies to 6 > 5) is a true statement.
Solution SetThe complete collection of all possible solutions to an inequality. This is often an infinite range of numbers.For x > 3, the solution set includes 3.1, 4, 5, 100, and all other numbers greater than 3.
Boundary PointThe value that separates the solutions from the non-sol...
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Core Formulas
The Substitution Principle
Given an inequality f(x) > c and a test value x = a, substitute 'a' into the inequality to get f(a) > c.
This is the core process for checking any potential solution. Replace the variable with the number you are testing.
The Truth Test
If f(a) > c is a true statement, then x = a is a solution. If it is a false statement, x = a is not a solution.
After substituting and simplifying, you must evaluate whether the resulting statement is mathematically correct. This determines if the tested value is a solution.
Boundary Point Inclusion Rule
For inequalities with > or <, the boundary point is NOT a solution. For inequalities with \geq or \leq, the boundary point IS a solution.
This rule helps you quickly check the specifi...
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Challenging
The number x = -3 is a solution to which of the following inequalities?
A.5 - 2x ≥ 11
B.x² + 2x > 5
C.-3x < 9
D.x² - 10 > 0
Challenging
What is the primary difference between the solution to the equation 2x = 10 and the solution set for the inequality 2x ≥ 10?
A.There is no difference; both have the solution x = 5.
B.The equation has one solution (x=5), while the inequality has two solutions (x=5 and x=-5).
C.The equation has no solution, while the inequality has an infinite solution set.
D.The equation has a single solution (x=5), while the inequality has an infinite solution set (all numbers greater than or equal to 5).
Challenging
Consider the inequality x² - 2x - 8 ≤ 0. The boundary points are x = -2 and x = 4. Which statement is true?
A.x = 4 is a solution, but x = 5 is not.
B.x = 5 is a solution, but x = 4 is not.
C.Both x = 4 and x = 5 are solutions.
D.Neither x = 4 nor x = 5 are solutions.
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Frequently asked questions
What grade level is "Identify solutions to inequalities"?
Identify solutions to inequalities is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Identify solutions to inequalities?
You'll be able to: Identify whether one group of objects has more, less, or the same number of objects as another group by counting; Explain, using drawings or manipulatives, why one event is more likely, less likely, or equally likely to occur….
Is "Identify solutions to inequalities" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Identify solutions to inequalities?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.