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Solving One-Step Equations Gangnam Style Video Step-by-step Vocabulary Inverse Operationtwo operations that “undo” each other, such as addition and subtraction Equivalent Equationsequations that have the same solution Solving an equation using subtraction Solve m + 12 = 7 First write the original equation. m + 12 = 7 Solving an equation using subtraction Solve m + 12 = 7 First write the original equation. m + 12 = 7 Then do the inverse operation. Subtract 12 from each side. m + 12 = 7 - 12 -12 Solving an equation using subtraction Solve m + 12 = 7 First write the original equation. m + 12 = 7 Then do the inverse operation. Subtract 12 from each side. m + 12 = 7 - 12 -12 Simplify m= -5 Check your solution. m + 12 = 7 Check your solution. m + 12 = 7 -5 + 12 =? 7 Substitute the solution for the variable Check your solution. m + 12 = 7 -5 + 12 =? 7 7 = 7 Simplify Check your solution. m + 12 = 7 -5 + 12 =? 7 7 = 7 YES! SOLUTION CONFIRMED! Solving an equation using addition Solve -2 = x - 9 Solving an equation using addition Solve -2 = x - 9 First write the original equation. Solving an equation using subtraction Solve -2 = x - 9 First write the original equation. -2 = x - 9 Then do the inverse operation. Which is what? Solving an equation using subtraction Solve -2 = x - 9 First write the original equation. -2 = x - 9 Then do the inverse operation. Add 9 to each side. -2 = x – 9 +9 +9 Solving an equation using subtraction Solve -2 = x - 9 First write the original equation. -2 = x - 9 Then do the inverse operation. Add 9 to each side. -2 = x – 9 +9 +9 Simplify +7=x Check your solution. -2 = x - 9 -2 =? 7 – 9 -2 = -2 YES! SOLUTION CONFIRMED! Writing and Solving an Equation You are traveling to Louisville, Kentucky. You have already traveled 122 miles, and you just passed a road sign that said Louisville is 76 miles away. How far is Louisville from the start of your trip? Writing and Solving an Equation Let d represent the distance from the start of your trip to Louisville. Write a verbal model. Distance from the - Distance traveled = Remaining distance start to Louisville Writing and Solving an Equation Let d represent the distance from the start of your trip to Louisville. Write a verbal model. Distance from the - Distance traveled = Remaining distance start to Louisville Use the verbal model to write an equation. d - 122 = 76 Writing and Solving an Equation Let d represent the distance from the start of your trip to Louisville. Write a verbal model. Distance from the - Distance traveled = Remaining distance start to Louisville Use the verbal model to write an equation. d - 122 = 76 Inverse operation + 122 + 122 Writing and Solving an Equation Let d represent the distance from the start of your trip to Louisville. Write a verbal model. - Distance traveled = Remaining distance Distance from the start to Louisville Use the verbal model to write an equation. d - 122 = 76 Inverse operation + 122 + 122 Simplify d = 198 Check your solution d = 198 d – 122 = 76 198 – 122 =? 76 76 = 76 YES! Louisville is 198 miles from the start of your trip. Your turn-Shopping Spree You have $37 left after shopping. You started with $85. How much money did you spend? Write a verbal model, equation, and then solve. Shopping Spree Money + Money left spent = Money started Let m be the money I spent. Shopping Spree Money + Money left spent = Money started Let m be the money I spent. 37 + m = 85 Shopping Spree Money + Money left spent = Money started Let m be the money I spent. 37 + m = 85 -37 - 37 Shopping Spree Money left + Money spent = Money started Let m be the money I spent. 37 + m = 85 -37 - 37 m = 48 Check your Solution 37 + m = 85 37 + 48 =? 85 85 = YES! 85 One more-Bike Race You are in a 50 km bike race. You have to bike 21 kilometers until you reach the finish line. How far have you already biked? Bike Race Total = distance Distance traveled d = distance traveled + Distance left Bike Race 50 = d + 21 - 21 - 21 29 = d Check 50 = d + 21 50 =? 29 + 21 50 = 50 YES! Equations-Multiplying & Dividing Gangnam Style Video Solving an Equation Using Division Solve 9x = -108 Solving an Equation Using Division Solve 9x = -108 Inverse Operation? Solving an Equation Using Division Solve 9x = -108 Inverse Operation? Divide by 9 Solving an Equation Using Division Solve 9x = -108 Inverse Operation? Divide by 9 9x = -108 9 9 Solving an Equation Using Division Solve 9x = -108 Inverse Operation? Divide by 9 9x = -108 9 9 x = -12 Check 9x = -108 9 (-12) =? -108 -108 = -108 YES! Solving an Equation Using Multiplication k =5 25 Solving an Equation Using Multiplication k =5 25 Inverse Operation? Solving an Equation Using Multiplication k =5 25 25 k =5 25 25 Solving an Equation Using Multiplication k =5 25 25 k =5 25 25 k = 125 Check k =5 25 125 =? 5 25 5 = 5 YES! Writing and Solving an Equation If you divide your camera film equally over your 7-day vacation, you will take 25 pictures a day. How many exposures do you have? Let e represent the number of exposures. Writing and Solving an Equation Total number = Number of days # of pics taken Writing and Solving an Equation Total number = Number of days e 7 = 25 # of pics taken Writing and Solving an Equation Total number = Number of days 7 e 7 = 25 # of pics taken 7 Writing and Solving an Equation Total number = Number of days 7 e 7 e = 25 = 175 # of pics taken 7 Check e 7 = 175 =? 7 25 25 Check e = 7 175 =? 7 25 = 25 25 25 You have 175 exposures. Your turn Your parents divide money evenly among you and your three siblings. Each of you receives $75. Find the total amount your parents gave. Let s equal the total amount of money your parents gave. s = 75 4 4 s = 75 4 4 4 s = 75 4 s = 300 4 Check s = 75 4 300 =? 75 4 Check s = 75 4 300 =? 75 4 75 = 75! One more You purchased 9 yards of fabric. The total cost is $45. Find the cost per yard of the fabric. Let f equal the cost per yard of fabric. 9f = 45 9f = 45 9 9 9f = 45 9 9 f = 5 Check 9f = 45 9 (5) =? 45 Check 9f = 45 9 (5) =? 45 45 = 45! Gangnam Style