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Questions and Answers
Which of the following represents an algebraic expression in one variable?
What is the algebraic expression in one variable for the following phrase: 'Five less than twice a number'?
Which of the following is an algebraic expression in one variable for the perimeter of a rectangle?
What is an example of an algebraic expression in one variable?
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Which of the following correctly represents an algebraic expression in one variable?
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Which of the following demonstrates an algebraic expression in one variable?
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Study Notes
Understanding Algebraic Expressions
- An algebraic expression consists of numbers, variables, and operators but does not include an equality sign.
- Expressions can include constants, coefficients, variables, and arithmetic operations like addition, subtraction, multiplication, and division.
Identifying One Variable Expressions
- A valid algebraic expression in one variable contains only one independent variable (e.g., x, y).
- Common representations include forms like ax + b, where a and b are constants.
Phrase Translation to Algebraic Expression
- "Five less than twice a number" translates to the expression: 2x - 5, where x represents the unknown number.
- This expression shows a relationship between a number and specific operations applied to it.
Perimeter of a Rectangle
- The perimeter P of a rectangle can be expressed in one variable using the formula: P = 2l + 2w, where l is the length and w is the width.
- If one dimension is expressed in terms of the other, it becomes a one-variable expression (e.g., if width w = x, then P = 2l + 2x).
Examples of Algebraic Expressions
- An example of an algebraic expression in one variable: 3x + 4 or x^2 - 7.
- Each example maintains a single variable while combining it with constants and mathematical operations.
Characteristics of Valid Algebraic Expressions
- A correctly structured algebraic expression must not contain equalities; instead, it focuses on expressing relationships using algebraic components.
- Examples to identify include factors, terms, and any numerical constants associated with a variable.
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Description
Test your knowledge of algebraic expressions in one variable with this quiz. Identify and create algebraic expressions for various mathematical situations, such as a phrase describing a number or the perimeter of a shape.
