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INTRODUCTION TO ALGEBRA COMMON MISTAKES 1 10/20/2009 Expressions vs. Equations How to tell the difference Expressions are a combinations of term(s) (a quantity expressed using numbers and/or variables) using the 4 basic operations (+, -, x, or /) Equations consist of expressions using an “=“ to set them equal to each other. Equations can be solved. 2 Complete Manual: ..\Introduction to Algebra Review.docx To view; right click and open the hyperlink 2 − 3 = 9x − x − 1 = 8x −1 =x 8 Common Mistakes Incorrectly combining terms when solving equations. ÷ Incorrect: x + 2 = 9 x + 3 is NO 10 x + 5 = 0 . Correct x + 2 = 9 x + 3 becomes 2 − 3 = 9 x − x − 1 = 8x −1 =x 8 10/20/2009 Expressions – Evaluating How to Evaluate Expressions To evaluate expressions, substitute the values where the variables occur. After substituting the given values into the expression, apply the rules for the Order of Operations to correctly simplify. 3 Complete Manual: ..\Introduction to Algebra Review.docx To view; right click and open the hyperlink Common Mistakes Incorrectly applying the Order of Operations to simplify an expression. Evaluate: − 3 x + 2 y − 1 if x = -2, y= -4 Incorrect: − 3 • −2 + 2 • −4 − 1 ≠ −6 − 8 − 1 ≠ −15 Correct: − 3 • −2 + 2 • −4 − 1 = 6 + −8 − 1 = −3 10/20/2009 Combining Like Terms How to combine like terms 4 Common Mistakes Like Terms are terms whose variables have the same exponent (also called the degree of the term). Not properly combining the Like Terms. 2 2 + + − Simplify: 2 x x 2 x x + 5 To combine like terms means to simplify an expression by combining the coefficients (number or constant in front of the variable) of like terms. Incorrect: =(2 x −1x ) + (1x + 2 x ) + 5 Complete Manual: ..\Introduction to Algebra Review.docx To view; right click and open the hyperlink 2 2 ≠ 4x + 5 3 Correct: =(2 x −1x ) + (1x + 2 x ) + 5 = x + 3x + 5 2 2 2 10/20/2009