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11-8

11-8. Solving Integer Equation. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Solving Integer Equations. 11-8. x. __. 5. Course 1. Warm Up Use mental math to find each solution. 1. 6 + x = 12 2. 3 x = 15 3. = 4 4. x – 8 = 12. x = 5. x = 6.

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11-8

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  1. 11-8 Solving Integer Equation Course 1 Warm Up Problem of the Day Lesson Presentation

  2. Solving Integer Equations 11-8 x __ 5 Course 1 Warm Up Use mental math to find each solution. 1.6 + x = 12 2. 3x = 15 3. = 4 4.x – 8 = 12 x = 5 x = 6 x = 20 x = 20

  3. Solving Integer Equations 11-8 Course 1 Problem of the Day Marie spent $15 at the fruit stand, buying peaches that cost $2 per container and strawberries that cost $3 per container. She bought the same number of containers of each fruit. How many containers each of peaches and strawberries did she buy? 3

  4. Solving Integer Equations 11-8 Course 1 Learn to solve equations containing integers.

  5. Solving Integer Equations 11-8 ? ? –13 = –13 –8 + (–5) = –13 Course 1 Additional Example 1A: Adding and Subtracting to Solve Equations Solve –8 + y = –13. Check your answer. –8 is added to y. –8 + y = –13 Subtracting –8 from both sides to undo the addition. + 8+ 8 y = –5 Check –8 + y = –13 Write the equation. Substitute –5 for y. –5 is a solution. 

  6. Solving Integer Equations 11-8 Helpful Hint Subtracting a number is the same as adding its opposite. To solve the equation on the previous slide using algebra tiles, you can subtract -8 tiles from both sides and then remove zero pairs. Course 1

  7. Solving Integer Equations 11-8 ? –6 –2 = –8 ? –8 = –8 Course 1 Additional Example 1B: Adding and Subtracting to Solve Equations Solve n – 2 = –8. Check your answer. 2 is subtracted from n. n – 2 = –8 Add 2 to both sides to undo the subtraction. + 2+ 2 n = –6 Check n –2 = –8 Write the equation. Substitute –6 for n. –6 is a solution. 

  8. Solving Integer Equations 11-8 ? ? -7 = -7 –2 + (–5) = –7 Course 1 Check It Out: Example 1A Solve –2 + y = –7. Check your answer. –2 is added to y. –2 + y = –7 Subtracting –2 from both sides to undo the addition is the same as adding +2. + 2+ 2 y = –5 Check –2 + y = –7 Write the equation. Substitute –5 for y. –5 is a solution. 

  9. Solving Integer Equations 11-8 ? –8 –6 = –14 ? –14= –14 Course 1 Check It Out: Example 1B Solve n – 6 = –14. Check your answer. 6 is subtracted from n. n – 6 = –14 Add 6 to both sides to undo the subtraction. + 6+ 6 n = –8 Check n –6 = –14 Write the equation. Substitute –8 for n. –8 is a solution. 

  10. Solving Integer Equations 11-8 ? 4(–5) = –20 ? –20 = –20 -20 4m ___ ___ 4 4 Course 1 Additional Example 2A: Multiplying and Dividing to Solve Equations Solve 4m = –20. Check your answer. m is multiplied by 4. Divide both sides by 4 to undo the multiplication. = m = –5 Check 4m = –20 Write the equation. Substitute –5 for m. –5 is a solution. 

  11. Solving Integer Equations 11-8 x 3 ? –21 ÷ 3 = –7 ? –7 = –7 x x __ __ 3 3 Course 1 Additional Example 2B: Multiplying and Dividing to Solve Equations Solve = –7. Check your answer. 3• = 3• (–7) x is divided by 3. Multiply both sides by 3 to undo the division. x = –21 Check = –7 Write the equation. Substitute –21 for x. –21 is a solution. 

  12. Solving Integer Equations 11-8 ? ? 3(–5) = –15 –15 = –15 -15 3n ___ ___ 3 3 Course 1 Check It Out: Example 2A Solve 3n = –15. Check your answer. n is multiplied by 3. Divide both sides by 3 to undo the multiplication. = n = –5 Check 3n = –15 Write the equation. Substitute –5 for n. –5 is a solution. 

  13. Solving Integer Equations 11-8 ? –24 ÷ 4 = –6 ? –6 = –6 y y y __ __ __ 4 4 4 Course 1 Check It Out: Example 2B Solve = –6. Check your answer. 4• = 4• (–6) y is divided by 4. Multiply both sides by 4 to undo the division. y = –24 Check = –6 Write the equation. Substitute –24 for y. –24 is a solution. 

  14. Solving Integer Equations 11-8 x __ 5 Course 1 Insert Lesson Title Here Lesson Quiz Solving each equation. 1. 5 + x = –6 2.y – 9 = –7 3. –6a = 24 4. = –9 5. A submarine captain sets the following diving course: dive 300 ft, stop, and then dive another 300 ft. If this pattern is continued, how many dives will be necessary to reach a location 3,000 ft below sea level? y = 2 x = –11 x = –45 a = –4 10

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