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Solving Linear Equations Definitions: Variable: a number that you don't know, often represented by "x" or "y" but any letter will do! Linear a mathematical statement that performs functions of addition, Expression: subtraction, multiplication, and division However, variable(s) in linear expressions • • • Cannot have exponents (or powers) For example, x squared or x 2 Cannot multiply or divide each other For example: "x" times "y" or xy; "x" divided by "y" or x/y Cannot be found under a root sign or square root sign (sqrt) For example: √ x or the "square root of x"; sqrt (x) These are examples of linear expressions: These are not linear expressions: (no exponents on x2 variables) x+4 2x + 4 (can't multiply two 2xy + 4 variables) 2x + 4y (can't divide two 2x / 4y variables) (no square root sign √ x on variables) Linear a mathematical expression that has an equal sign and linear expressions Equation: Solving example #1: find x if 2x + 4 = 10 linear equation steps to solve math First step is to isolate "x" to one side of the equation by subtracting 4 from both sides: 2x + 4 - 4 = 10 - 4 2x + 4 = 10 Second step is to divide both sides by 2: 2x = 6 2x / 2 = 6 / 2 x=3 Check your work with the original equation: Solving example #2: find x if 3x 2x + 4 = 10 (2 * 3) + 4 = 10 6 + 4 = 10 - 4 = -10 (using negatives) linear equation steps to solve math First step is to isolate "x" to one side of the equation by adding 4 to both sides: 3x - 4 + 4 = -10 + 4 3x - 4 = -10 Second step is to divide both sides by 3: 3x / 3 = -6 / 3 x = -2 Check your work with the original equation: (3 * -2) - 4 = -10 -6 - 4 = -10 3x = -6 Solving example #3: find x if: 4x - 4y = 8 (using more than one variable) linear equation steps to solve math 4x - 4y = 8 First step is to isolate "x" to one side of the equation by adding 4y to both sides: 4x - 4y + 4y = 8 + 4y 4x = 8 + 4y Second step is to divide both sides by 4: 4x / 4 = (8 + 4y) / 4 x=2+y Check your work with the original equation: 4 * (2 + y) - 4y = 8 8 + 4y - 4y = 8 8=8 Solving example #4: find x if: x + 32 = 12 linear equation steps to solve math x + 32 = 12 (Note: since the square is First step is to square the on the number number: and not on the variable, x + 32 = 12 x + 9 = 12 the expression qualifies as a linear expression. Second step is to subtract both sides by 9: x + 9 - 9 = 12 - 9 x =3 Check your work with the original equation: 3 + 32 = 12 3 + 9 = 12 12 = 12 Flash exercise by Jay Austin and Jordan Noll, College of Design; Brad Hokanson, faculty, College of Design, University of Minnesota, St. Paul, MN; with refinements by: Steve Kladstrup, Independent Flash Developer, Minneapolis, MN. Reference: www.studygs.net