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Simplify.

Exercise. Simplify. 5 + 7 − 7. 5. Exercise. Simplify. − 12 − 16 + 16. −12. Exercise. Simplify. 136,798 − 3,479 + 3,479. 136,798. Exercise. Simplify. 7 × 8 ÷ 8. 7. Exercise. Simplify. 375 ÷ 15 × 15. 375. Equation.

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Simplify.

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  1. Exercise Simplify. 5 + 7 − 7 5

  2. Exercise Simplify. −12 − 16 + 16 −12

  3. Exercise Simplify. 136,798− 3,479 + 3,479 136,798

  4. Exercise Simplify. 7 × 8 ÷ 8 7

  5. Exercise Simplify. 375 ÷ 15 × 15 375

  6. Equation An equation is a mathematical sentence that contains an equal sign.

  7. Solution A solution is a number that, when substituted for a variable, makes a mathematical sentence true.

  8. Inverse Operations Inverse operations are operations that undo one another.

  9. Inverse Operations Addition/Subtraction Multiplication/Division

  10. Exercise Is this an equation? If so, what is the solution? 2x + 3 no

  11. Exercise Is this an equation? If so, what is the solution? x + 3 = 4 yes; 1

  12. Exercise Is this an equation? If so, what is the solution? 4x2 − 5 no

  13. Exercise Is this an equation? If so, what is the solution? n − 5 = 5 yes; 10

  14. Addition Property of Equality For all integers a, b, and c, if a = b, then a + c = b + c.

  15. Example 1 Solve x− 6 = 10, and check the solution. x = 16

  16. Example 2 Solve a+ 39 = 17, and check the solution. a= -22

  17. Solving an Equation Involving Addition or Subtraction • Determine what operation must be performed in order to isolate the variable on one side of the equation.

  18. Solving an Equation Involving Addition or Subtraction • Undo addition by subtracting, or undo subtracting by adding. • Remember that what you do to one side of the equation you must do to the other side also.

  19. 15 = y + 11 y+ 11 = 15

  20. Symmetric Property of Equality If a = b, then b = a.

  21. Example 3 Solve 47 = m + 3, and check the solution. m = 44

  22. Subtracting a “−” is the same as . 3 − (−6)

  23. Adding a “−” is the same as . 3 + (−6)

  24. Example 4 Solve y − (−7) = −18, and check the solution. y = −25

  25. Example 5 Solve z + (−32) = −19, and check the solution. y = 13

  26. Example 6 Write each word phrase as a mathematical expression. Use n for the variable. a. four more than a number n + 4 b. a number increased by ten n + 10

  27. Example 6 c. five less than a number n − 5 d. a number decreased by seven n − 7 e. seventeen decreased by a number 17 − n

  28. Example 7 Write an algebraic expression for the number of nickels Sergei has and the number Kimberly has. Sergei has 8 more than Evan, and Kimberly has 6 fewer than Evan. Use x as the variable.

  29. Example 7 Let x = the number of nickels Evan has. Sergei has x + 8 nickels. Kimberly has x − 6 nickels.

  30. Example 8 Write an equation for the sentence “A number decreased by three is sixteen.” Let n = the number. n − 3 = 16

  31. Example 9 Write an equation for the sentence “Seven dollars more than the cost of the shoes is ninety-eight dollars.” Let c = the cost. c + 7 = 98

  32. Exercise Solve. −5 + (s + 2) = −9(8)

  33. Exercise Solve. (17 − 12) − (−a) = 125 − 250

  34. Exercise Solve. −6y + 9 +7y−4 = −8 + (−41)

  35. Exercise Solve. 23 + c− 7 + 2 = 7 − 61

  36. Exercise Solve. d+ [17 − (−12)] = 5 − (−58)

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