1. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solving Equations by Adding, Subtracting, Multiplying and Dividing Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Algebra 1

2. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Warm Up Evaluate. 1. 0.51 + (0.29) Give the opposite of each number. 2. 83.  Evaluate each expression for a = 3 and b = 2. 4. a + 55. 12  b 0.8 2 3 –8 148 2 3

3. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve one-step equations in one variable by using addition or subtraction. Solve one-step equations in one variable by using multiplication or division. Objective

4. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 An equation is a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, isolate the variable. A variable is isolated when it appears by itself on one side of an equation, and not at all on the other side.

5. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Inverse Operations OperationInverse Operation AdditionSubtraction Addition Isolate a variable by using inverse operations which "undo" operations on the variable. An equation is like a balanced scale. To keep the balance, perform the same operation on both sides.

6. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Example 1A: Solving Equations by Using Addition Since 8 is subtracted from y, add 8 to both sides to undo the subtraction. y – 8 = 24 + 8 + 8 y = 32 Check y – 8 = 24 32 – 8 24 24 To check your solution, substitute 32 for y in the original equation.

7. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Example 1B: Solving Equations by Using Addition = z 3 4 To check your solution, substitute for z in the original equation. 3 4 + 7 16 + 7 = z – 7 16 5 Check = z – 7 16 5 3 4 5 7 – 5 5 Since is subtracted from z, add to both sides to undo the subtraction. 7 16 7

8. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Check It Out! Example 2c Since 6 is added to t, subtract 6 from both sides to undo the addition. 6 + t = 14 – 6 t = 8 Check 6 + t = 14 6 + 8 14 14 To check your solution, substitute 8 for t in the original equation.

9. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve –2.3 + m = 7. Check your answer. Check It Out! Example 3a Since –2.3 is added to m, add 2.3 to both sides. –2.3 + m = 7 +2.3 + 2.3 m = 9.3 Check –2.3 + m = 7 –2.3 + 9.3 7 7 To check your solution, substitute 9.3 for m in the original equation.

10. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Over 20 years, the population of a town decreased by 275 people to a population of 850. Write and solve an equation to find the original population. Example 4: Application Substitute 275 for d and 850 for c. + 275 p =1125 p – d = c original population minus current population decrease in population is p – 275 = 850 Since 275 is subtracted from p, add 275 to both sides to undo the subtraction. p – 275 =850 The original population was 1125 people.

11. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 A person's maximum heart rate is the highest rate, in beats per minute, that the person's heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find a person's age if the person's maximum heart rate is 185 beats per minute. Check It Out! Example 4

12. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Check It Out! Example 4 Continued a + r = 220 age added to 220 maximum heart rate is Write an equation to represent the relationship. – 185 a = 35 a + 185 = 220 Substitute 185 for r. Since 185 is added to a, subtract 185 from both sides to undo the addition. a + r = 220 A person whose maximum heart rate is 185 beats per minute would be 35 years old.

13. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Inverse Operations OperationInverse Operation MultiplicationDivision Multiplication Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.

14. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Check It Out! Example 1a Since p is divided by 5, multiply both sides by 5 to undo the division. p = 50 10 To check your solution, substitute 50 for p in the original equation. = 10 p 5 10 50 5 Check = 10 p 5

15. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Check It Out! Example 1b Since y is divided by 3, multiply both sides by 3 to undo the division. –39 = y –13 To check your solution, substitute –39 for y in the original equation. –13 = y 3 –13 –39 3 y Check –13 = 3

16. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12 108 To check your solution, substitute 12 for y in the original equation. 9y = 108 9(12) 108 Check 9y = 108

17. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Check your answer. Example 2B: Solving Equations by Using Division Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. 0.8 = v –4.8 To check your solution, substitute 0.8 for v in the original equation. –4.8 = –6v –4.8 –6(0.8) Check –4.8 = –6v

18. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

19. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Solve the equation. Example 3A: Solving Equations That Contain Fractions w = 24 20 To check your solution, substitute 24 for w in the original equation. w = 20 5 6 Check w = 20 5 6 The reciprocal of is. Since w is multiplied by, multiply both sides by. 5 6 6 5 5 6 6 5 20

20. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Check It Out! Example 3b j = 1 Solve the equation. = 4j4j 6 2 3 is the same as j. 4 6 4j 6 The reciprocal of is. Since j is multiplied by, multiply both sides by. 4 6 4 6 6 4 6 4

21. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Example 4: Application Write an equation to represent the relationship. Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro put $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 1 4 one-fourth times earnings equals college fund m = $1140 Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns.

22. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Check it Out! Example 4 Write an equation to represent the relationship. The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began. Distance divided by 3 equals height in thousands of feet 15 = h Substitute 45 for d. The plane was flying at 15,000 ft when the descent began.

23. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Lesson Quiz Solve each equation. 1. r – 4 = –8 2. 3. m + 13 = 58 6. This year a high school had 578 sophomores enrolled. This is 89 less than the number enrolled last year. Write and solve an equation to find the number of sophomores enrolled last year. –4 45 s – 89 = 578; s = 667

24. Solving Equations by Adding or Subtracting Holt McDougal Algebra 1 Lesson Quiz: Part 2 Solve each equation. 1. 3. 8y = 4 4. 126 = 9q 5. 21 –14 40