 Here are a few review concepts before we start solving equations!

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Presentation transcript:

 Here are a few review concepts before we start solving equations!

 Parentheses  Exponents  Multiply/Divide from left to right  Add/Subtract from left to right

 The properties of real numbers allow us to manipulate expressions and equations and find the values of a variable.

 Natural numbers are the counting numbers.  Whole numbers are natural numbers and zero.  Integers are whole numbers and their opposites.  Rational numbers can be written as a fraction.  Irrational numbers cannot be written as a fraction.  All of these numbers are real numbers.

Subsets of the Real Numbers I - Irrational Z - Integers W - Whole N - Natural Q - Rational

 To solve an equation, find replacements for the variables to make the equation true.  Each of these replacements is called a solution of the equation.  Equations may have {0, 1, 2 … solutions.

 A variable is a letter which represents an unknown number. Any letter can be used as a variable.  An algebraic expression contains at least one variable.  Examples: a, x+5, 3y – 2z

 A verbal expression uses words to translate algebraic expressions.  Example: “The sum of a number and 3” represents “ n+3. ”  An equation is a sentence that states that two mathematical expressions are equal.  Example: 2x-16=18

 Simplify each side of the equation, if needed, by distributing or combining like terms.  Move variables to one side of the equation by using the opposite operation of addition or subtraction.  Isolate the variable by applying the opposite operation to each side.  First, use the opposite operation of addition or subtraction.  Second, use the opposite operation of multiplication or division.  Check your answer

● “y” is the variable. ● Add 6 to each side to isolate the variable. ● Now divide both sides by 3. ● The answer is 5. ● Check the answer by substituting it into the original equation.

 Since 4 ≠ 5, this can never be true and therefore the solution is no solution.  Since 0 = 0, this is always true and therefore the solution is infinitely many solutions.

 Try the sample problems from the notes document before you begin the assignment. Make sure you check your solutions in my notebook at the desk before you begin the assignment!