Questions and Answers
What is a linear equation in one variable?
What does it mean to combine like terms?
To add or subtract the coefficients of terms that have the same variables raised to the same powers.
What is the numerical coefficient in the term 4x^2y?
4
What are like terms?
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Constants are considered like terms.
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What is the distributive property in the form of combining like terms?
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The letters in algebraic terms and expressions are called __________.
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The numbers with letters in algebraic terms are called __________.
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What does PBBEMDAS stand for?
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What happens when simplifying an expression like 3x + 25 - x?
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Study Notes
Linear Equations
- A linear equation in one variable is represented by the formula: ax + b = c.
Combining Like Terms
- Terms consist of multiplication and/or division involving constants and variables.
- Constant terms involve only real numbers (e.g., -14 or 5.6).
- Exponents indicate repeated factors in a term, such as 2x^5 or 13x^2y.
Numerical Coefficient
- The numerical factor in a variable term is known as the coefficient.
- For example, in 4x^2y, the coefficient is 4.
- If no coefficient is present, it is assumed to be 1, e.g., x = 1·x or -y = -1·y.
Like Terms
- Like terms share the same variables raised to identical powers (e.g., 2x^2 and 3x^2).
- Constants are categorized as like terms.
Simplifying Expressions
- To simplify expressions with like terms, combine them by adding or subtracting their coefficients while maintaining the common variable expression.
Distributive Property
- Combining like terms involves using the distributive property: ba + ca = (b + c)a.
Algebraic Expression
- An algebraic expression includes one or more algebraic terms and operational symbols, without an equals sign.
- Examples of algebraic expressions: 3x^2 + 5y + 47 or -2x.
Variables
- Variables are letters representing numbers that can vary based on the expression.
Coefficients
- Coefficients are numbers associated with variables (e.g., in 3x^2, 3 is the coefficient).
Simplifying Expression Process
- Simplification involves performing indicated operations, often resulting in collecting like terms.
- Example: 3x + 25 - x simplifies to 2x + 25.
PBBEMDAS
- Order of operations is denoted by: Parenthesis, Brackets, Braces, Exponents, Multiply/Divide, Add/Subtract.
- Phrase for remembering: "Please Be Beautiful, Excuse (My Dear) Aunt Sally."
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Description
This quiz covers concepts related to linear equations, combining like terms, and simplifying algebraic expressions. Students will explore numerical coefficients, like terms, and the distributive property to enhance their understanding of algebraic manipulation.
