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#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. http://www.mathslideshows.com #2 SOLUTION A solution is the final answer to an equation, or the value of the variable. Example: 3a = 30 a = 10 10 is the solution http://www.mathslideshows.com #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! http://www.mathslideshows.com #4 Add the same number to both sides. a – 15 = 22 Get the variable alone. +15 +15 Add 15 to both sides. a = 37 +15 and -15 cancel out 37 - 15 = 22 Show your check! 22 = 22 Finish your check! http://www.mathslideshows.com #5 Divide the same number into both sides 5x = 40 5 5 x = 8 5 • 8 = 40 40 = 40 Get the variable alone. Divide 5 into both sides. 5 divided by 5 cancels out to 1. Show your check! Finish your check! http://www.mathslideshows.com #6 Multiply the same number to both sides x = 20 Get the variable alone. 2 2• x = 20 •2 Multiply both sides by 2. 2 2 divided by 2 cancels out to 1. x = 40 40 20 2 20 = 20 Show your check! Finish your check! http://www.mathslideshows.com #7 Use inverse operations to solve integer equations. a – -3 = 21 + -3 + -3 a = 18 18 - -3 = 21 21 = 21 Get the variable alone. Add -3 to both sides. + -3 and – -3 cancel out Check your answer Finish your check http://www.mathslideshows.com #8 Divide the same number into both sides -8x = -64 Get the variable alone. -8 Divide -8 into both sides. x = -8 8 -8 8 = -64 -64 = -64 -8 divided by -8 cancel out to 1. Check your answer. Finish your check. http://www.mathslideshows.com Algebra Tile Equations #9 2x + 2 x x = 4 + = ++ + ++ Algebra 2x + 2 = 4 -2 = -2 2x = 2 2 2 x=1 Draw a picture. Take away 2 from both sides. Divide both sides in half. http://www.mathslideshows.com Algebra Balance Scales #10 2x + 6 = 3x + 4 1) Draw a picture. x ++ = x ++ ++ x 2) Take away 2x from both sides. x x ++ ++ Algebra 3) Take away 4 from both sides. 2x + 6 = 3x + 4 -2x = -2x 6 = 1x + 4 -4 -4 2 = x http://www.mathslideshows.com #11 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or division second, by using inverse operations. http://www.mathslideshows.com #12 2 Step Subtract/Multiply Equation 3m - 10 = 17 +10 +10 __ 3m 3 m __ = 27 3 =9 3(9) – 10 =17 27 – 10 =17 17 =17 Get the variable alone. Add 10 to both sides. +10 and -10 cancel out Divide both sides by 3 3 divided by 3 cancel to 1 Show your check. Finish your check. http://www.mathslideshows.com #13 x 2 x 2 x 2( 2 x + 6 = 14 -6 -6 =8 Get the variable alone. Subtract 6 from both sides. + 6 and -6 cancel out. ) = 2 8 Multiply both sides by 2. = 16 16 + 6 = 14 2 8 + 6 = 14 14 = 14 2 divided by 2 cancels out Show your check. Finish your check. http://www.mathslideshows.com #14 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. http://www.mathslideshows.com #15 Solve Multi Step Equations 1) 5x 2x 6 21 2) 6x 7 x 18 3x 6 21 6 6 5x 7 18 7 7 5x 25 5 5 x5 3x 15 3 3 x5 http://www.mathslideshows.com #16 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 http://www.mathslideshows.com #17 3 - 2x = 11 -3 -3 -__ 2x =__ 8 -2 -2 x = -4 1)Get the variable alone, even if the coefficient is negative. 2)Subtract 3 from both sides. 3) +3 and -3 cancel out 4) Divide both sides by - 2 5) -2 divided by –2 cancel out 6) Show your check. 3 - 2(-4) = 11 3 + 8 = 11 11 = 11 7) Finish your check. http://www.mathslideshows.com #18 2x + 2 = 4x – 2 x x 2x + 2 -2x 2 +2 4 2 2 x ++ ++ = x = 4x - 2 -2x = 2x - 2 +2 = 2x 2 = x http://www.mathslideshows.com x x –+ –+ Move the smaller number of x’s to one side #19 1) Get rid of the parenthesis by distributing 2) Combine like terms 3) Move the smaller number of x’s to one side 4) Move all numbers to the other side 5) Get x all by itself 6) Check your answer in the original equation Circle answer. Show work in the check! http://www.mathslideshows.com #20 5(m - 6) = 10 5m - 30 = 10 + 30 +30 5m = 40 Check in the original equation! Get rid of parenthesis first by distributing. 5 5 m=8 5(8 - 6) = 10 5(2) = 10 10 = 10 http://www.mathslideshows.com Do PEMDAS in the check! #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 Add 4 to both sides. 2 2 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 http://www.mathslideshows.com Extra http://www.mathslideshows.com #1 Equations An equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign. 12 – 3 = 9 3a = 30 Numerical Algebraic http://www.mathslideshows.com #7 2 y 10 3 Multiply both sides by the reciprocal of the fraction. 32 3 3 y 10 2 2 3 2 cancel out to 1. 2 3 Multiply the numerators. Multiply the denominators. 10 3 y 1 2 30 y 2 15 Simplify http://www.mathslideshows.com 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 . http://www.mathslideshows.com For more information on Math Slideshows visit: http://www.mathslideshows.com/ http://www.mathslideshows.com