Algebraic Expressions and Properties

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What is an algebraic expression?

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An algebraic expression is a mathematical phrase that can include numbers, variables (like x or y), and operations (like addition, subtraction, multiplication, and division). For example, 3x + 5 is an algebraic expression.

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What is the Commutative Property?

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The Commutative Property states that the order in which two numbers are added or multiplied does not change the result. For example, a + b = b + a and ab = ba.

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What is the Associative Property?

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The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For example, (a + b) + c = a + (b + c) and (ab)c = a(bc).

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

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What does it mean to simplify an expression?

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To simplify an expression means to combine like terms and perform any operations to make the expression as simple as possible. For example, 2x + 3x simplifies to 5x.

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What is a variable in algebra?

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A variable is a symbol, usually a letter, that represents one or more numbers. For example, in the expression 2x + 3, x is a variable.

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What is a coefficient?

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A coefficient is a number that is multiplied by a variable in an algebraic expression. For example, in 4x, 4 is the coefficient.

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What is a constant?

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A constant is a fixed value that does not change. For example, in the expression 3x + 5, the number 5 is a constant.

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What is an equation?

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An equation is a mathematical statement that asserts the equality of two expressions. For example, 2x + 3 = 7 is an equation.

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution. For example, 2x + 3 = 7 and x = 2 are equivalent equations.