Students will use inverse operations to solve one-step equations. 8x = -72 m + 18 = 3 Students will use inverse operations to solve one-step equations. x + 4 = 12 m – 18 = - 3 3p = - 27

ONE-STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced.

Keep the scale balanced. If we add 3 apples to this side… What must we do to this side?

Keep the scale balanced. What must we do to this side? If we subtract 3 bananas from this side…

ONE STEP EQUATIONS To solve one step equations, you need to ask three questions about the equation: What is the variable? What operation is performed on the variable? What is the inverse operation? (The one that will “undo” what is being done to the variable)

INVERSE OPERATIONS The inverse operation of addition is… SUBTRACTION The inverse operation of subtraction is… ADDITION The inverse operation of multiplication is… DIVISION The inverse operation of division is… MULTIPLICATION

1-Step Equations with addition Example 1 Solve x + 3 = 9 What is the variable? The variable is x. What operation is being performed on the variable? Addition. What is the inverse operation? Subtraction. The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal. Using the subtraction property of equality, subtract 3 from both sides of the equation. x + 3 = 9 - 3 - 3 x = 6 You can check ALL answers. Start by writing the original problem. x + 3 = 9 Plug in your answer. 6 + 3 = ? CORRECT! 9

Do/UNDO Approach     X=6 69     Inverse 99 UNDO 99

Practice: 1-step Equations with addition 1. m + 9 = 3 3. g + 4 = -12 j + (-3) = 1 4. c + 5 = 0 + (+3) - 9 - 9 - (-3) - (-3) m = -6 j = 4 check: -6 + 9 = ? check: 4 + (-3) = ? 3 = 3  1 = 1  - 4 - 4 - 5 - 5 g = -16 c = - 5 check: -16 + 4 = ? check: - 5 + 5 = ? -12 = -12  0 = 0 

1-Step Equations with subtraction   What is the variable? The variable is x. What operation is being performed on the variable? Subtraction. What is the inverse operation? Addition. The addition property of equality tells us to add the same thing on both sides to keep the equation equal. Using the addition property of equality, add 4 to both sides of the equation. x – 4 = 7 + 4 + 4 x = 11 Check your work! x – 4 = 7 Plug in your answer. 11 – 4 = ? CORRECT! 7

Do/Undo Approach             Inverse   UNDO  

Practice: 1-step Equations with subtraction f – 3 = - 5 2. n – 18 = 2 3. g – 8 = -2 4. m – 11 = 1 + 3 + 3 + 18 +18 f = -2 n = 20 check: -2 – 3 = ? check: 20 – 18 = ? -5 = -5  2 = 2  + 8 + 8 + 11 +11 g = 6 m = 12 check: 6 – 8 = ? check: 12 – 11 = ? -2 = -2  1 = 1 

1-Step Equations with multiplication Example 3 Solve 2x = 12 What is the variable? The variable is x. What operation is being performed on the variable? Multiplication. What is the inverse operation? Division The division property of equality tells us to divide the same thing on both sides to keep the equation equal. Using the division property of equality, divide both sides of the equation by 2. 2x = 12 2 2 x = 6 CHECK: REMEMBER: The fraction means DIVIDE! 2x = 12 2(6) = ? CORRECT! 12

Do/Undo Approach             Inverse   UNDO  

Practice: 1-step Equations with multiplication 3a = -18 2. -4n = -32 3. 5m = -45 4. -3x = 3 3 3 -4 -4 a = -6 n = 8 Check: 3 (-6) = ? Check: -4 (8) = ? -18 = -18  -32 = -32  5 5 -3 -3 m = -9 x = -1 Check: 5 (-9) = ? Check: -3 (-1) = ? -45 = -45  3 = 3 

1-Step Equations with division Example 4 Solve   What is the variable? The variable is x. What operation is being performed on the variable? Division. What is the inverse operation? Multiplication Using the multiplication property of equality, multiply both sides of the equation by 6. The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal. 6 • = 8 •6 x = 48 CHECK: = 8 48 = ? 6 Correct! 8

Do/Undo Approach     48       Inverse   UNDO  

Practice: 1-step Equations with division (-4) (-4) 1. 3. 2. 4. (3) (3) x = -36 b = 18 Check: Check: 6 = 6  9 = 9  (-5) (-5) (-8) (-8) x = 10 k = -8 Check: Check: -2 = -2  1 = 1 

Summary When solving one-step equations, always use the “inverse operation” to undo the operation that is done on the variable. ALWAYS CHECK YOUR WORK!

Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. Solve one-step equations. 1 2 3 1. Isabella is baking muffins. The recipe calls for 8 cups of sugar. Isabella has already added 3 cups of sugar. How many more cups of sugar does she need to add? 2. Yesterday, Samuel had $7. He was given more money today and now has $10. How much money was Samuel given today? 3. Shannon had some money in her pocket. She received $4 for school supplies. She now has $11. How much money did she start with? 4. Jessie had a few marbles. He earned 5 of them during a game and now has 8. How many marbles did Jessie start with? m + 7 = 10 m + 7 = 10 c + 3 = 8 c + 3 = 8 3 + 7 = 10 - 3 - 3 5 + 3 = 8 - 7 - 7 10 = 10 8 = 8 c = 5 m = 3 Isabella needs to add __________________. 5 cups of sugar Samuel was given ________________ today. $3 m + 4 = 11 m + 4 = 11 m + 5 = 8 m + 5 = 8 7 + 4 = 11 3 + 5 = 8 - 4 - 4 - 5 - 5 11 = 11 8= 8 m = 7 m = 3 Shannon started with __________________. $7 Jessie started with _____________________. 3 marbles

Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. Solve one-step equations. 1 2 3 Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. 1. Binders cost $2 each. If Miguel has $12, how many binders can he buy? 2. A box of pencils has 6 pencils inside. If Rosalina has 24 pencils, how many boxes does she have? 3. Isabella gave out muffins to her 6 friends. If each friend was given 4 muffins, how many muffins did Isabella give out? 4. Ricky and his two friends earned money doing chores for his neighbor. After splitting the money, they each got $7. How much money did they earn together? 2b = 12 2b = 12 6b = 24 6b = 24 2 2 2(6) = 12 6 6 6(4) = 24 12 = 12 b = 6 24 = 24 b = 4 Miguel can buy ______________________. 6 binders She has ______________________. 4 boxes of pencils m 4 = 6 4 ● ● 4 m 3 = 7 3 ● ● 3 m = 24 m = 21 6 = 6 7 = 7 Isabella gave out ______________________. 24 muffins Ricky and his friends earned _____________. $21

Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. Solve one-step equations. 1 2 3 1. Larissa has 17 dollars. She gets her allowance. Now she has 28 dollars. How much was her allowance? 2. A set of colored pencils has 45 pencils taken out. There are currently 29 pencils left. How many pencils were there originally? 3. Hugh earns $8 for mowing lawns. Last month, he earned $48. How many lawns did he mow? 4. Thomas and his 5 friends made cookies. They shared them equally and each got 13. How many cookies did they make altogether? 17 + a = 28 p - 45 = 29 - 17 - 17 17 + 11 = 28 + 45 + 45 74 - 45 = 29 a = 11 28 = 28 29 = 29 n = 74 Larissa’s allowance is ______________________. $11 There were __________________ originally. 74 pencils in the set ● 6 6 ● 8 8 8m = 48 8(6) = 48 c = 78 b = 6 48 = 48 13 = 13 Hugh mowed ______________________. 6 lawns Thomas and his friends made __________________. 78 cookies