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Lesson 1a Notes - Solving Multi-Step Linear Equations

Learn to solve multi-step linear equations of one variable with terms, like terms, properties of equality, and solution types. Explore examples and practice to master the concepts effectively.

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Lesson 1a Notes - Solving Multi-Step Linear Equations

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  1. Lesson 1a Notes - Solving Multi-Step Linear Equations - To solve linear equations of one variable

  2. Definitions Algebraic Expression – mathematical expression involving at least one unknown value Algebraic Equation – mathematical equation involving at least one unknown value (a true mathematical statement)

  3. Definitions Terms – parts of the expression separated by +/- signs Like Terms – terms which are “alike” (same exponent on same variable) and can be combined

  4. +/-/×/÷ Properties of Equality Adding, subtracting, multiplying or dividing the same number to both sides of the equation results in another equivalent equation

  5. Definitions Solution – a real number that can replace the variable in an equation and make the statement true

  6. Examples • 4x + 8x = 17x – 9 – 1 • 6 – (4 + m) = 8m – 2(3m + 5)

  7. Conditional Equations • A linear equation with one solution • When solved, x = a, where a is a real number (zero included)

  8. Identity vs. Contradiction Identity Equation Absurd Equation No solutions, solution set Ø When solved, final line is false, a = b, where a and b are real numbers • Infinite solutions, solution set {all real #’s} • When solved, final line is true, a = a, where a is a real number

  9. Examples • 5(x + 2) – 2(x + 1) = 3x + 1 • -4y + 3(y – 2) = -(y + 2)

  10. Homework p. 68 #12-36 ev, 65-74 all

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