Algebraic Concepts

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Term

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A single number, variable, or a combination of both with multiplication or division. (e.g., 3x, -5, 7y²)

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Coefficient

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The number in front of a variable. (e.g., in 4x, the coefficient is 4)

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Constant

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A number without a variable. (e.g., 7 in 3x + 7)

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Like Terms

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Terms that have the same variable raised to the same exponent. (e.g., 2x and 5x are like terms, but 3x² and 3x are not)

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Expression

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A mathematical phrase containing numbers, variables, and operations, but no equal sign. (e.g., 3x + 5)

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Simplifying Expressions: Combine like terms

Example: 3x + 4 + 5x - 2

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Solution: (3x + 5x) + (4 - 2) = 8x + 2

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Distributive Property

Example: 2(x+3)

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Solution: 2x + 6

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Factoring (Reverse of Distribution)

Example: 6x + 12;

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Solution: 6(x + 2)

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Solving One-Step Equations:
Example: x + 5 = 12

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Subtract 5 from both sides;

Solution: x = 7

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Solving Two-Step Equations: Example: 2x + 3 = 11

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Solution: Subtract 3 to get 2x = 8, then divide by 2 to find x = 4.