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

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

Solving Integer Equations Course 1 11-8 Solving Integer Equations 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

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

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

Solving Integer Equations Course 1 11-8 Solving Integer Equations 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. Helpful Hint

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

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

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

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

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

Solving Integer Equations Course 1 11-8 Solving Integer Equations 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. 3n 3 ___ -15 3 ___ = n = –5 Check 3n = –15 Write the equation. 3(–5) = –15 ? Substitute –5 for n. –15 = –15 ? –5 is a solution. 

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

Solving Integer Equations Insert Lesson Title Here Course 1 11-8 Solving Integer Equations 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? x = –11 y = 2 x 5 __ a = –4 x = –45 10