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    Algebra

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    guyusher02

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    Algebra

    Uploaded by

    guyusher02
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    4 views2 pages

    Algebra

    Uploaded by

    guyusher02

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    © All Rights Reserved
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    of 2

    Sure! Here’s a quick rundown of some key algebra concepts and formulas.

    If you need more


    detail on any topic, just let me know!

    ### Basic Concepts

    1. **Variables and Constants**


    - **Variable**: A symbol (usually a letter) that represents an unknown value (e.g., \( x \), \( y \)).
    - **Constant**: A fixed value (e.g., 5, -3).

    2. **Expressions and Equations**


    - **Expression**: A combination of variables, constants, and operators (e.g., \( 3x + 4 \)).
    - **Equation**: A statement that two expressions are equal (e.g., \( 2x + 3 = 7 \)).

    3. **Terms and Coefficients**


    - **Term**: A single mathematical expression (e.g., \( 3x \), \( -2 \)).
    - **Coefficient**: The number in front of a variable (e.g., in \( 5x \), 5 is the coefficient).

    ### Operations with Algebraic Expressions

    1. **Addition and Subtraction**


    - Combine like terms: \( 3x + 4x = 7x \) and \( 5 - 2 = 3 \).

    2. **Multiplication**
    - Use distributive property: \( a(b + c) = ab + ac \).
    - Example: \( 2(x + 3) = 2x + 6 \).

    3. **Division**
    - Divide each term in the numerator by the denominator: \( \frac{4x + 8}{4} = x + 2 \).

    ### Solving Equations

    1. **One-Step Equations**
    - Solve for \( x \): \( x + 5 = 12 \) → \( x = 12 - 5 \) → \( x = 7 \).

    2. **Two-Step Equations**
    - Solve for \( x \): \( 2x + 3 = 11 \)
    - Subtract 3 from both sides: \( 2x = 8 \)
    - Divide by 2: \( x = 4 \)

    3. **Multi-Step Equations**
    - Example: \( 3(x - 2) + 4 = 16 \)
    - Distribute: \( 3x - 6 + 4 = 16 \)
    - Combine like terms: \( 3x - 2 = 16 \)
    - Solve for \( x \): \( 3x = 18 \) → \( x = 6 \)
    ### Factoring

    1. **Greatest Common Factor (GCF)**


    - Factor out the largest common factor from each term: \( 6x + 9 = 3(2x + 3) \).

    2. **Quadratic Expressions**
    - **Factoring by Grouping**: \( x^2 + 5x + 6 \) can be factored as \( (x + 2)(x + 3) \).
    - **Difference of Squares**: \( a^2 - b^2 = (a + b)(a - b) \).

    ### Functions and Graphs

    1. **Linear Functions**
    - **Slope-Intercept Form**: \( y = mx + b \) where \( m \) is the slope and \( b \) is the
    y-intercept.
    - Example: For \( y = 2x + 1 \), slope \( m = 2 \) and y-intercept \( b = 1 \).

    2. **Quadratic Functions**
    - **Standard Form**: \( y = ax^2 + bx + c \)
    - The graph is a parabola. The vertex can be found using \( x = -\frac{b}{2a} \).

    ### Systems of Equations

    1. **Substitution Method**
    - Solve one equation for one variable, then substitute into the other equation.

    2. **Elimination Method**
    - Add or subtract equations to eliminate one variable, then solve for the remaining variable.

    ### Inequalities

    1. **Solving Inequalities**
    - Solve similarly to equations but remember to reverse the inequality sign when multiplying or
    dividing by a negative number.

    2. **Graphing Inequalities**
    - Represent solutions on a number line or coordinate plane, shading the appropriate region.

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