Algebra: Writing Expressions, Equations & Inequalities

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Slide 1  Introduction to Algebra
 Writing Expressions, Equations & Inequalities

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.

Slide 3  Vocabulary

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.

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.)

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.

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”)

Slide 9  Evaluating Expressions
 When we are given an expression and a solution, we can evaluate that expression for the given solution.
 Example:

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!

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!