Algebra: Writing Expressions, Equations & Inequalities

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Algebra: Writing Expressions, Equations & Inequalities

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  1. Introduction to Algebra

    Slide 1 - Introduction to Algebra

    • Writing Expressions, Equations & Inequalities
  2. What is algebra?

    Slide 2 - What is algebra?

    • Al · ge · bra
    • (noun) the part of mathematics in which letters and other general symbols are used to represent numbers and quantities.
  3. Vocabulary

    Slide 3 - Vocabulary

  4. Variables & Constants

    Slide 4 - Variables & Constants

    • Variables: a quantity that could change (or vary) during the calculations. In this class, a variable can be represented by any lower case letter (but it’s best to avoid o and l)
    • Constant: a quantity that will not change (is constant) during the calculations. This shows up as a number.
  5. Coefficients & Operators

    Slide 5 - Coefficients & Operators

    • Coefficients: constants that come before a variable. They tell us how many of that variable are present. For example “four x’s” is written 4x
    • Operators: mathematical symbols that represent operations to be performed (adding, subtracting, etc.)
  6. Expressions & Equations

    Slide 6 - Expressions & Equations

    • Expressions and equations are like mathematical sentences.
    • An expression has no equals sign, but an equation does…
    • For example:
    • “Four of a number added to 10”
    • 4n + 10  this is an expression
    • Another example:
    • “Four of a number added to 10 is 30”
    • 4n + 10 = 30  this is an equation
    • Notice that “a number” is shown as a variable in the examples. We don’t know what that number is yet, so we write is as a variable. When we read an expression or equation, we say “a number” outloud.
  7. Equations & Inequalities

    Slide 7 - Equations & Inequalities

    • An equation has an equal sign. An inequality has an inequality sign.
    • ≥ “greater than or equal to”
    • > “greater than” (but not equal to)
    • ≠ “not equal to”
    • < “less than” (but not equal to)
    • ≤ “less than or equal to”
    • Example:
    • Read from left to right:
    • “a number is greater than five”
    • Notice that the larger part of the sign points to the larger amount (or “the alligator eats the bigger meal”)
  8. Evaluating Expressions

    Slide 9 - Evaluating Expressions

    • When we are given an expression and a solution, we can evaluate that expression for the given solution.
    • Example:
  9. Mentally Solving Equations

    Slide 11 - Mentally Solving Equations

    • Equations can be solved mentally use “try, check, revise”.
    • Step 1. Read aloud: “12 minus a number is 10”
    • Step 2. Estimate a solution and try it: “Two? 12 minus 2 is 10” CHECK!
  10. Mentally Solving Inequalities

    Slide 13 - Mentally Solving Inequalities

    • Inequalities can also be solved mentally use “try, check, revise”.
    • Step 1. Read aloud: “A number is less than 20”
    • Step 2. Estimate a solution and try it: “Fifteen? 15 is less than 20?” CHECK!