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Equations

#1. Equations. An equation is a mathematical statement that shows 2 quantities are equal . An equation contains an equal sign. 12 – 3 = 9 Numerical 3a = 30 Algebraic. To solve any equation use inverse operations . Your goal is to get the variable all by itself. #2.

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Equations

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  1. #1 Equations • An equation is a mathematical statement that • shows 2 quantities are equal. An equation • contains an equal sign. 12 – 3 = 9 Numerical 3a = 30 Algebraic To solve any equation use inverse operations. Your goal is to get the variable all by itself.

  2. #2 SOLUTION • A solutionis the final answer to an • equation, or the value of the variable. Example: 3a = 30 a = 10 10 is the solution

  3. To Solve An Addition Equation #3 Subtract the same number from both sides. • m+ 8 = 12 Get the variable alone. – 8 –8 Subtract 8 from both sides. m = 4 +8 and -8 cancel each other out. 4+ 8 = 12 Show your check. 12 = 12 Finish your check!

  4. To Solve a Subtraction Equation #4 Add the same number to both sides. Get the variable alone. • a – 15 = 22 +15 +15 Add 15 to both sides. +15 and -15 cancel out a = 37 37- 15 = 22 Show your check! Finish your check! 22 = 22

  5. #5 To Solve a Multiplication Equation Divide the same number into both sides • 5x = 40 Get the variable alone. 5 5 Divide 5 into both sides. x = 8 5 divided by 5 cancels out to 1. 5 • 8 = 40 Show your check! 40 = 40 Finish your check!

  6. #6 To Solve a Division Equation Multiply the same number to both sides x 2 Get the variable alone. • = 20 2• •2 x 2 Multiply both sides by 2. = 20 2 divided by 2 cancels out to 1. x = 40 Show your check! Finish your check! 20 = 20

  7. #7 Integer Equation Useinverse operations to solve integer equations. Get the variable alone. • a – -3 = 21 + -3 + -3 Add -3 to both sides. + -3 and – -3 cancel out a = 18 18- -3 = 21 Check your answer 21 = 21 Finish your check

  8. #8 Integer Multiplication Equation Divide the same number into both sides • -8x = -64 Get the variable alone. -8 -8 Divide -8 into both sides. x = 8 -8 divided by -8 cancel out to 1. Check your answer. -8 8 = -64 -64 = -64 Finish your check.

  9. #9 Algebra Tile Equations • 2x + 2 = 4 + + Draw a picture. + + = + + Take away 2 from both sides. Algebra 2x + 2 = 4 -2 = -2 Divide both sides in half. 2 2 2x = 2 x = 1

  10. #10 Algebra Balance Scales 2x + 6 = 3x + 4 1) Draw a picture. + + + + x + + + + x 2) Take away 2x from both sides. = x x + + 3) Take away 4 from both sides. x Algebra 2x + 6 = 3x + 4 -2x = -2x 6 = 1x + 4 -4 -4 2 = x

  11. #11 Solve 2 Step Equations 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division second, by using inverse operations.

  12. #12 2 Step Subtract/Multiply Equation Get the variable alone. +10 +10 Add 10 to both sides. • 3m - 10 = 17 __ __ 3 3 3m = 27 +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 =17 Show your check. 27 – 10 =17 Finish your check. 17 =17

  13. #13 2 Step ADD/DIVIDE Equation x 2 Get the variable alone. - 6 - 6 Subtract 6 from both sides. • + 6 = 14 x 2 = 8 + 6 and -6 cancel out. x 2 Multiply both sides by 2. ( ) = 8 2 2 2 divided by 2 cancels out x = 16 16 2 Show your check. + 6 = 14 8 + 6 = 14 Finish your check. 14 = 14

  14. #14 Rules for Solving Equations 1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. 4) Easiest to undo add/subtract before multiply/divide.

  15. Solve Multi Step Equations #15

  16. #16 Multiple Step Equations 3x + 4 = 5x - 10 Steps -3x -3x 1) Get all of the x’s on 1 side. 4 = 2x - 10 2) Subtract 3x from both sides. +10 +10 3) Add 10 to both sides. 14 = 2x 2 2 4) Divide both sides by 2 7 = x

  17. #17 Negative Coefficient Equations 1)Get the variable alone, even if the coefficient is negative. -3 -3 • 3 - 2x = 11 - 2x = 8 __ __ -2 -2 2)Subtract 3 from both sides. 3) +3 and -3 cancel out x = -4 4) Divide both sides by - 2 3 - 2(-4) = 11 5) -2 divided by –2 cancel out 3+ 8 = 11 6) Show your check. 11 = 11 7) Finish your check.

  18. #18 Variable on Both Sides Picture 2x + 2 = 4x – 2 – x + + x x ++ – + + = x x x 2x + 2 = 4x - 2 -2x -2x Move the smaller number of x’s to one side 2 = 2x - 2 +2 +2 4 = 2x 2 2 2 = x

  19. Steps To Solve Equations #19 • Get rid of the parenthesis by distributing • Combine like terms • Move the smaller number of x’s to one side • Move all numbers to the other side • Get x all by itself • Check your answer in the original equation • Circle answer. Show work in the check!

  20. #20 Equations With Parenthesis 5(m - 6) = 10 Get rid of parenthesis first by distributing. 5m - 30 = 10 + 30 +30 5m = 40 5 5 Check in the original equation! Do PEMDAS in the check! m = 8 5(8- 6) = 10 5(2) = 10 10 = 10 

  21. Variable On Both Sides #21 8x - 4 = 3(2x + 8) Get rid of the parenthesis. 8x - 4 = 6x + 24 Get the variables on one side. -6x -6x Subtract 6x from both sides. 2x - 4 = 24 6x and –6x cancel out + 4 + 4 2x = 28 __ __ 2 2 Add 4 to both sides. Divide both sides by 2. x = 14 8(14) - 4 = 3(2 14+8) Show your check! 112 - 4 = 3(36) Finish your check! 108 = 108

  22. Extra

  23. #1 Equations • An equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign. 12 – 3 = 9 Numerical 3a = 30 Algebraic

  24. To Solve a Fraction Equation #7 Multiply both sides by thereciprocal of the fraction. Multiply thenumerators.Multiply thedenominators. Simplify

  25. If you have trouble viewing you need MathType software: To see all math formulas correctly you need to install MathType software, similar to equation editor and is available for free at Design Science website.

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