Mathematics
Grade 9
15 min
Write the subtraction sentence - up to two digits
Write the subtraction sentence - up to two digits
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Introduction & Learning Objectives
Learning Objectives
Translate verbal phrases involving subtraction into algebraic expressions.
Identify and apply the correct inequality symbol (>, <, ≥, ≤) based on contextual keywords.
Construct a one-variable linear inequality from a real-world scenario that involves a subtraction operation.
Model constraints in a problem using constants up to two digits within a subtraction-based inequality.
Differentiate between a subtraction expression, a subtraction equation, and a subtraction inequality.
Define the variable in a given problem and write a complete subtraction sentence as a linear inequality.
You have $85 in your account and need to withdraw some cash. How can you write a mathematical sentence to make sure you have at least $20 left? 🏦
In this tutorial, we will...
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Key Concepts & Vocabulary
TermDefinitionExample
Linear InequalityA mathematical sentence that uses an inequality symbol (<, >, ≤, ≥) to compare two expressions, where the variable has an exponent of one.x - 15 > 40
Subtraction Sentence (Algebraic)A complete mathematical statement that models a situation where a quantity is taken away from an unknown value, resulting in a comparison.A starting amount 's' decreased by 25 is at most 50, written as s - 25 ≤ 50.
VariableA symbol, usually a letter, that represents an unknown or changing quantity.In the sentence 'p - 10 > 22', 'p' is the variable.
ConstantA fixed numerical value that does not change. In our problems, these will be numbers up to two digits.In 'x - 18 ≥ 75', the numbers 18 and 75 are constants.
Inequality...
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Core Formulas
General Form: Subtraction Inequality
x - a ≥ b
This is the basic structure. 'x' is the initial unknown amount, 'a' is the quantity being subtracted, and 'b' is the value it's being compared to. The symbol (≥) can be replaced with >, <, or ≤ depending on the problem's context.
Translation Rule: 'Decreased By' or 'Minus'
'A number x decreased by a' → x - a
Use this rule when you see phrases like 'decreased by', 'minus', 'less', or 'take away'. The quantity being subtracted (a) comes after the minus sign.
Translation Rule: 'Less Than'
'a less than a number x' → x - a
Be careful with this phrasing. The number mentioned first in the s...
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Challenging
The initial temperature of a chemical solution is 't' degrees Celsius. A cooling agent is added, causing the temperature to drop by 22 degrees. For the experiment to be valid, the final temperature must not exceed 50 degrees. Which inequality represents this condition?
A.t - 22 > 50
B.t - 22 ≥ 50
C.t - 22 < 50
D.t - 22 ≤ 50
Challenging
Given the inequality 'p - 35 ≥ 60', which scenario is the most plausible model and correctly identifies what 'p' represents?
A.Scenario: A price 'p' is discounted by $60. The final price is at least $35. 'p' is the original price.
B.Scenario: A plane's altitude 'p' decreases by 35 feet. The new altitude is at least 60 feet. 'p' is the initial altitude.
C.Scenario: You have 'p' points. You earn 35 more. Your total is at least 60. 'p' is your starting score.
D.Scenario: From a budget of $60, you spend 'p' dollars. You have at least $35 left. 'p' is the amount spent.
Challenging
A company's revenue is 'r' million dollars and its costs are $85 million. The profit, which is revenue minus costs, must exceed last year's profit of $95 million. Which subtraction sentence correctly models the required revenue?
A.r - 85 > 95
B.r - 95 > 85
C.85 - r > 95
D.95 - r > 85
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