11 8 Solving Integer Equation Warm Up Problem

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

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

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 Course 1

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

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

11 -8 Solving Integer Equations 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

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

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

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

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

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

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

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

11 -8 Solving Insert Lesson Integer. Title Equations Here Lesson Quiz Solving each equation. 1. 5 + x = – 6 x = – 11 2. y – 9 = – 7 y = 2 3. – 6 a = 24 a = – 4 x 4. __ = – 9 x = – 45 5 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? 10 Course 1