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Transcript
11-8 Solving Integer Equations Warm Up Use mental math to find each solution. 1. 6 + x = 12 x = 6 2. 3x = 15 x 3. __ = 4 5 4. x – 8 = 12 x = 20 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 11-8 Solving Integer Equations Sunshine State Standards Preview of MA.7.A.3.3 Formulate and use different strategies to solve one-step…linear equations. Also Preview of MA.7.A.3.2 11-8 Solving Integer Equations Vocabulary Identity Property 11-8 Solving Integer Equations Additional Example 1A: Adding and Subtracting to Solve Equations Solve –8 + y = –13. Check your answer. –8 +8 + y = –13 y is added to –8. + 8 Add 8 to both sides. y = –5 Check –8 + y = –13 ? –8 + (–5) = –13 Write the equation. Substitute –5 for y. ? –13 = –13 –5 is a solution. 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 add eight yellow tiles to both sides and then remove zero pairs. 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 Add 2 to both sides to undo the subtraction. n = –6 +2 Check n – 2 = –8 ? –6 – 2 = –8 ? –8 = –8 Write the equation. Substitute –6 for n. –6 is a solution. 11-8 Solving Integer Equations Check It Out: Example 1A Solve –2 + y = –7. Check your answer. –2 + y = –7 +2 +2 y is added to –2. Add 2 to both sides. y = –5 Check –2 + y = –7 –2 + ? (–5) = –7 ? -7 = -7 Write the equation. Substitute –5 for y. –5 is a solution. 11-8 Solving Integer Equations Check It Out: Example 1B 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 Write the equation. Substitute –8 for n. –8 is a solution. 11-8 Solving Integer Equations Additional Example 2A: Multiplying and Dividing to Solve Equations Solve 4m = –20. Check your answer. -20 4m ___ ___ = 4 4 m = –5 Check 4m = –20 ? 4(–5) = –20 ? –20 = –20 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 2B: 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 Write the equation. Substitute –21 for x. –21 is a solution. 11-8 Solving Integer Equations Check It Out: Example 2A Solve 3n = –15. Check your answer. –15 3n ___ = ___ 3 3 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. 3(–5) = –15 ? –15 = –15 –5 is a solution. 11-8 Solving Integer Equations Check It Out: Example 2B 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 Write the equation. Substitute –24 for y. –24 is a solution.