Mathematics
Grade 9
15 min
Solve one-step linear inequalities addition and subtraction
Solve one-step linear inequalities addition and subtraction
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1
Introduction & Learning Objectives
Learning Objectives
Define and identify the components of a one-step linear inequality.
Solve one-step linear inequalities using the Addition Property of Inequality.
Solve one-step linear inequalities using the Subtraction Property of Inequality.
Represent the solution set of a linear inequality on a number line.
Translate a real-world scenario into a one-step linear inequality involving addition or subtraction.
Verify a potential solution to a one-step linear inequality.
Ever wonder how much you can spend on a game and still have enough money left for snacks? 🎮 That's an inequality!
This tutorial will teach you how to solve simple inequalities using addition and subtraction. Unlike equations that have one answer, inequalities have a whole range of solutions. Masterin...
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Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two expressions using an inequality symbol, showing that one expression is less than, greater than, less than or equal to, or greater than or equal to another.x + 5 > 10
Inequality SymbolsThe symbols used to show the relationship between quantities that are not equal.< (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to)
Solution SetThe set of all numbers that make an inequality true. This is often an infinite range of numbers.For x > 3, the solution set includes 4, 5, 3.1, and all other numbers greater than 3.
VariableA symbol, usually a letter, that represents an unknown number or a range of numbers.In y - 7 ≤ 2, 'y' is the variable.
Number Line GraphA visual re...
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Core Formulas
Addition Property of Inequality
If a < b, then a + c < b + c
You can add the same number to both sides of an inequality, and the inequality symbol remains the same. This rule applies to all four inequality symbols (<, >, ≤, ≥).
Subtraction Property of Inequality
If a < b, then a - c < b - c
You can subtract the same number from both sides of an inequality, and the inequality symbol remains the same. This rule also applies to all four inequality symbols (<, >, ≤, ≥).
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Challenging
The solution to the inequality x + k < 15 is x < 8. What is the value of k?
A.7
B.-7
C.23
D.-23
Challenging
If a, b, and c are real numbers and a - c > b, which of the following statements MUST be true?
A.a > b
B.b > a
C.a + c > b
D.a > b + c
Challenging
Which real-world scenario could be modeled by the inequality n - 15 ≥ 60, where n is the number of tickets you started with?
A.After selling 15 tickets, you have at most 60 tickets left.
B.After selling 15 tickets, you have at least 60 tickets left.
C.You started with 15 tickets and sold some to have 60 left.
D.You sold 60 tickets and have fewer than 15 left.
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