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Learn to solve equations using addition and subtraction. Solving Addition and Subtraction Equations. 1-3. Pre-Algebra. 100. Solving Addition and Subtraction Equations. 1-3. = 50. 2. Pre-Algebra.

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  1. Learn to solve equations using addition and subtraction. Solving Addition and Subtraction Equations 1-3 Pre-Algebra

  2. 100 Solving Addition and Subtraction Equations 1-3 = 50 2 Pre-Algebra An equation uses an equal sign to show that two expressions are equal. All of these are equations. 3 + 8 = 11 r + 6 = 14 24 = x – 7 To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

  3. ? ? ? Solving Addition and Subtraction Equations 13= 15 x + 8 = 15 5 + 8 = 15 1-3 Pre-Algebra Example 1: Determining Whether a Number is a Solution of an Equation Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 5 for x.  So 5 is not solution.

  4. ? ? ? Solving Addition and Subtraction Equations 15= 15 x + 8 = 15 7 + 8 = 15 1-3 Pre-Algebra Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 7 for x.  So 7 is a solution.

  5. ? ? ? Solving Addition and Subtraction Equations 31= 15 x + 8 = 15 23 + 8 = 15 1-3 Pre-Algebra Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. Substitute 23 for x.  So 23 is not a solution.

  6. Solving Addition and Subtraction Equations 1-3 Pre-Algebra Addition and subtraction are inverseoperations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

  7. + z + 4 + 4 Solving Addition and Subtraction Equations + z ADDITION PROPERTY OF EQUALITY 1-3 Words Numbers Algebra Pre-Algebra To solve a subtraction equation, like y− 15 = 7, you would use the Addition Property of Equality. You can add the same number to both sides of an equation, and the statement will still be true. 2 + 3 = 5 x = y x = y 2 + 7 = 9

  8. −z − 3 − 3 Solving Addition and Subtraction Equations −z SUBTRACTION PROPERTY OF EQUALITY 1-3 Words Numbers Algebra Pre-Algebra There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality. You can subtract the same number from both sides of an equation, and the statement will still be true. 4 + 7 = 11 x = y x = y 4 + 4 = 8

  9. ? Solving Addition and Subtraction Equations ? 10 + 8 = 18 18 = 18 1-3 Pre-Algebra Example 2A: Solving Equations Using Addition and Subtraction Properties Solve. A. 10 + n = 18 10 + n = 18 –10 –10 Subtract 10 from both sides. 0 + n = 8 Identity Property of Zero: 0 + n = n. n = 8 Check 10 + n = 18 

  10. ? Solving Addition and Subtraction Equations ? 17 – 8 = 9 9 = 9 1-3 Pre-Algebra Example 2B: Solving Equations Using Addition and Subtraction Properties Solve. B. p – 8 = 9 p – 8 = 9 + 8 + 8 Add 8 to both sides. p + 0= 17 Identity Property of Zero: p + 0 = p. p = 17 Check p – 8 = 9 

  11. ? ? Solving Addition and Subtraction Equations 22 = 33 – 11 22 = 22 1-3 Pre-Algebra Example 2C: Solving Equations Using Addition and Subtraction Properties Solve. C. 22 = y – 11 22 = y – 11 + 11 + 11 Add 11 to both sides. 33 = y + 0 Identity Property of Zero: y + 0 = 0. 33 = y Check 22 = y – 11 

  12. Solving Addition and Subtraction Equations 1-3 Pre-Algebra Addition and subtraction are inverseoperations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

  13. ? ? ? Solving Addition and Subtraction Equations 5 = 13 x – 4 = 13 9 – 4 = 13 1-3 Pre-Algebra Try This: Example 1 Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. Substitute 9 for x.  So 9 is not a solution.

  14. ? ? ? Solving Addition and Subtraction Equations 13 = 13 x – 4 = 13 17 – 4 = 13 1-3 Pre-Algebra Try This: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. Substitute 17 for x.  So 17 is a solution.

  15. ? ? ? Solving Addition and Subtraction Equations 23 = 13 x – 4 = 13 27 – 4 = 13 1-3 Pre-Algebra Try This: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 17, or 27 Substitute each value for x in the equation. Substitute 27 for x.  So 27 is not a solution.

  16. ? Solving Addition and Subtraction Equations ? 10 + 14 = 29 29 = 29 1-3 Pre-Algebra Try This: Example 2A Solve. A. 15 + n = 29 15 + n = 29 –15 –15 Subtract 15 from both sides. 0 + n = 14 Identity Property of Zero: 0 + n = n. n = 14 Check 15 + n = 29 

  17. ? Solving Addition and Subtraction Equations ? 13 – 6 = 7 7 = 7 1-3 Pre-Algebra Try This: Example 2B Solve. B. p – 6 = 7 p – 6 = 7 + 6 + 6 Add 6 to both sides. p + 0= 13 Identity Property of Zero: p + 0 = p. p = 13 Check p – 6 = 7 

  18. ? ? Solving Addition and Subtraction Equations 44 = 67 – 23 44 = 44 1-3 Pre-Algebra Try This: Example 2C Solve. C. 44 = y – 23 44 = y – 23 + 23 + 23 Add 23 to both sides. 67 = y + 0 Identity Property of Zero: y + 0 = 0. 67 = y Check 44 = y – 23 

  19. odometer reading at the beginning of the trip Solving Addition and Subtraction Equations odometer reading at the end of the trip 1-3 miles traveled Pre-Algebra Example 3A A. Thomas took a 34-mile trip in his car, and the odometer showed 16,550 miles at the end of the trip. What was the original odometer reading? + = + = 34 Solve: x 16,550 x + 34 = 16,550 –34 – 34 Subtract 34 from both sides. x + 0 = 16,516 x = 16,516 The original odometer reading was 16,516 miles.

  20. Solving Addition and Subtraction Equations increase in population population after increase 1-3 initial population Pre-Algebra Example 3B B. From 1980 to 2000, the population of a town increased from 895 residents to 1125 residents. What was the increase in population during that 20-year period? + = + = n Solve: 895 1125 895 + n = 1125 –895 – 895 Subtract 895 from both sides. 0 + n = 230 n = 230 The increase in population was 230.

  21. Solving Addition and Subtraction Equations increase in water level water level after increase 1-3 initial water level Pre-Algebra Try This: Example 3B B. From June to July, the water level in a lake has increased from 472 feet to 502 feet. What was the increase in water level during that 1-month period? + = + = n Solve: 472 502 472 + n = 502 –472 – 472 Subtract 472 from both sides. 0 + n = 30 n = 30 The increase in water level was 30 feet.

  22. 100 Solving Addition and Subtraction Equations 1-3 = 50 2 Pre-Algebra An equation uses an equal sign to show that two expressions are equal. All of these are equations. 3 + 8 = 11 r + 6 = 14 24 = x – 7 To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

  23. Solving Addition and Subtraction Equations 1-3 Pre-Algebra Addition and subtraction are inverseoperations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

  24. ? Solving Addition and Subtraction Equations ? 10 + 8 = 18 18 = 18 1-3 Pre-Algebra Example 2A: Solving Equations Using Addition and Subtraction Properties Solve. A. 10 + n = 18 10 + n = 18 –10 –10 Subtract 10 from both sides. 0 + n = 8 Identity Property of Zero: 0 + n = n. n = 8 Check 10 + n = 18 

  25. ? Solving Addition and Subtraction Equations ? 17 – 8 = 9 9 = 9 1-3 Pre-Algebra Example 2B: Solving Equations Using Addition and Subtraction Properties Solve. B. p – 8 = 9 p – 8 = 9 + 8 + 8 Add 8 to both sides. p + 0= 17 Identity Property of Zero: p + 0 = p. p = 17 Check p – 8 = 9 

  26. ? ? Solving Addition and Subtraction Equations 22 = 33 – 11 22 = 22 1-3 Pre-Algebra Example 2C: Solving Equations Using Addition and Subtraction Properties Solve. C. 22 = y – 11 22 = y – 11 + 11 + 11 Add 11 to both sides. 33 = y + 0 Identity Property of Zero: y + 0 = 0. 33 = y Check 22 = y – 11 

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