Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1

Use mental math to find each solution. 1. 6 + x = 12 2. 3x = 15 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 2

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 3

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

Vocabulary Identity Property 5

Additional Example 1A: Adding and Subtracting to Solve Equations Solve –8 + y = –13. Check your answer. –8 + y = –13 y is added to –8. + 8 + 8 Add 8 to both sides. y = –5 Check –8 + y = –13 Write the equation. –8 + (–5) = –13 ? Substitute –5 for y. –13 = –13 ? –5 is a solution.  6

Subtracting a number is the same as adding its opposite 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. Helpful Hint 7

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.  8

Solve –2 + y = –7. Check your answer. Check It Out: Example 1A Solve –2 + y = –7. Check your answer. –2 + y = –7 y is added to –2. + 2 + 2 Add 2 to both sides. y = –5 Check –2 + y = –7 Write the equation. –2 + (–5) = –7 ? Substitute –5 for y. -7 = -7 ? –5 is a solution.  9

Solve n – 6 = –14. Check your answer. 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.  10

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.  11

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.  12

Solve 3n = –15. Check your answer. 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.  13

Solve = –6. Check your answer. 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 = –6 y 4 __ Write the equation. –24 ÷ 4 = –6 ? Substitute –24 for y. –6 = –6 ? –24 is a solution.  14

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 15

Lesson Quiz Solving each equation. 1. 5 + x = –6 2. y – 9 = –7 5. A deep-sea submersible follows this 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 16

Lesson Quiz for Student Response Systems 1. Solve the equation. 7 + y = –29 A. y = 36 B. y = 22 C. y = –36 D. y = –22 17

Lesson Quiz for Student Response Systems 2. Solve the equation. z – 5 = –19 A. z = 14 B. z = 26 C. z = –26 D. z = –14 18

Lesson Quiz for Student Response Systems 3. Solve the equation. –9z = 72 A. z = –8 B. z = –63 C. z = –81 D. z = –648 19

Lesson Quiz for Student Response Systems 4. Jacob is 12 years older than Andrew. If Jacob’s age is now 30, what is Andrew’s age? A. 16 years B. 18 years C. 40 years D. 42 years 20