Math series Solving Linear Equations Linear Equation: a mathematical expression that has an equal sign and linear expressions Variable: a number that you dont know, often represented by x or y but any letter will do! Variable(s) in linear expressions Cannot have exponents (or powers) For example, x squared or x2 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 x; sqrt (x) Linear Expression: a mathematical statement that performs functions of addition, subtraction, multiplication, and division These are examples of linear expressions: x + 4 2x + 4 2x + 4y These are not linear expressions: x2 (no exponents on variables) 2xy + 4 (cant multiply two variables) 2x / 4y (cant divide two variables) √x (no square root sign on variables) Solve these linear equations by clicking and dragging a number to the other side of the equal sign. Remember that you are isolating the unknown X to solve the problem. (More examples are provided below.) More examples: Linear equation, solving example #1: Find x if: 2x + 4 = 10 1.)Isolate x to one side of the equation by subtracting 4 from both sides: 2x + 4 - 4 = 10 - 4 2x = 6 2).Divide both sides by 2: 2x / 2 = 6 / 2 x = 3 3.)Check your work with the original equation: 2x + 4 = 10 (2 * 3) + 4 = 10 6 + 4 = 10 Linear equation, solving example #2: Find x if: 3x - 4 = -10 (using negatives) 1.)Isolate x to one side of the equation by adding 4 to both sides: 3x - 4 + 4 = -10 + 4 3x = -6 2.)Divide both sides by 3: 3x / 3 = -6 / 3 x = -2 3.)Check your work with the original equation: (3 * -2) - 4 = -10 -6 - 4 = -10 Linear equation, solving example #3: Find x if: 4x - 4y = 8 (using more than one variable) 1.)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 2.)Second step is to divide both sides by 4: 4x / 4 = (8 + 4y) / 4 x = 2 + y 3.)Check your work with the original equation: 4 * (2 + y) - 4y = 8 8 + 4y - 4y = 8 8 = 8 Linear equation, solving example #4: Find x if: x + 32 = 12 Note: since the square is on the number and not on the variable, the expression qualifies as a linear expression 1.)First step is to square the number: x + 32 = 12 x + 9 = 12 2.)Second step is to subtract both sides by 9: x + 9 - 9 = 12 - 9 x = 3 3.)Check your work with the original equation: 3 + 32 = 12 3 + 9 = 12 12 = 12 Math series Math exams | Solving linear equations | Solving math word problems, introdution | Word problems, exercise I | Word problems, II | Word problems, III | Evaluating algebraic expressions | Creating and developing spreadsheets | P.E.M.D.A.S.: 2nd exercise | P.E.M.D.A.S.: 3rd exercise | Sudoku 数独 Thanks to John Hocutt for his contributions to this page: John is a professional math & science tutor based in Redondo Beach, CA 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. StumbleUpon
Posted on: Sun, 25 Jan 2015 03:03:50 +0000
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