2 5 Solving Equations Containing Integers 2 5

2 -5 Solving Equations Containing Integers

2 -5 Solving Equations Containing Integers Additional Example 1 A: Solving Addition and Subtraction Equations Solve each question. Check each answer. – 6 + x = – 7 +6 +6 x = – 1 Check Add 6 to both sides to isolate the variable. – 6 + x = – 7 ? – 6 + (– 1) = – 7 ? – 7 = – 7 Substitute – 1 for x. True.

2 -5 Solving Equations Containing Integers Additional Example 1 B: Solving Addition and Subtraction Equations Solve each equation. Check each answer. p + 5 = – 3 + (– 5) +(– 5) Add – 5 to both sides. p = – 8 Check p + 5 = – 3 ? – 8 + 5 = – 3 ? – 3 = – 3 Substitute – 8 for p. True.

2 -5 Solving Equations Containing Integers Additional Example 1 C: Solving Addition and Subtraction Equations Solve each equation. Check each answer. y – 9 = – 40 +9 +9 Check Add 9 to both sides. y = – 31 y – 9 = – 40 ? – 31 – 9 = – 40 ? – 40 = – 40 Substitute – 31 for y. True.

2 -5 Solving Equations Containing Integers Check It Out: Example 1 Solve each equation. Check your answer. A. y – 7 = – 34 +7 +7 y = – 27 B. – 7 + b = 9 +7 +7 b = 16

2 -5 Solving Equations Containing Integers Check It Out: Example 1 Solve each equation. Check each answer. C. m – 5 = – 12 +5 +5 m = – 7

2 -5 Solving Equations Containing Integers Additional Example 2 A: Solving Multiplication and Division Equations Solve each equation. Check each answer. b =6 – 5 b (– 5) – 5 = (– 5)6 b = – 30 Multiply both sides by – 5.

2 -5 Solving Equations Containing Integers Additional Example 2 A Continued Check b =6 – 5 ? – 30 = 6 – 5 6 = 6 Substitute – 30 for b. True. b = 6. – 5

2 -5 Solving Equations Containing Integers Additional Example 2 B: Solving Multiplication and Division Equations Solve each equation. Check each answer. – 400 = 8 y 8 8 – 50 = y Divide both sides by 8.

2 -5 Solving Equations Containing Integers Additional Example 2 B: Solving Multiplication and Division Equations Check – 400 = 8 y Substitute – 50 for y. ? – 400 = 8(– 50) – 400 = – 400 True.

2 -5 Solving Equations Containing Integers Check It Out: Example 2 A Solve each equation. Check your answer. c = – 12 4 4 c = (4)(– 12) 4 c = – 48

2 -5 Solving Equations Containing Integers Check It Out: Example 2 B Solve each equation. Check your answer. 6 a = – 366 366 6 a =– 6 6 a = – 61

2 -5 Solving Equations Containing Integers Check It Out: Example 2 C Solve each equation. Check your answer. – 12 d = 144 – 12 d = – 12

2 -5 Solving Equations Containing Integers Check It Out: Example 2 D Solve each equation. Check your answer. h = – 7 9 9 h = (9)(– 7) 9 h = – 63

2 -5 Solving Equations Containing Integers Additional Example 3: Business Application In 2007, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in 2006. What was the profit in 2006? Let p represent the profit in 2006 (in millions of dollars). 2007 profit 300 is =100 million More than + 100 300 = 100 + p – 100 200 = p The profit was $200 million in 2006 profit p

2 -5 Solving Equations Containing Integers Check It Out: Example 3 A In July, a department store made a profit of $50 thousand. This amount was $17 thousand less than the profit in June. What was the profit in June? Let p represent the profit in June (in thousands of dollars). Profit in July = p – 17 Profit in July = $50 thousand

2 -5 Solving Equations Containing Integers Check It Out: Example 3 A continued p – 17 = 50 + 17 p = 67 The profit in June was $67 thousand.

2 -5 Solving Equations Containing Integers Check It Out: Example 3 B In 2008, a manufacturer made a profit of $450 million. A negative profit is considered a loss. This amount was $125 million more than the profit in 2007. What was the profit in 2007? Let p represent the profit in 2007 (in millions of dollars). Profit in 2008 = p + 125 Profit in 2008 = $– 450

2 -5 Solving Equations Containing Integers Check It Out: Example 3 B Continued p + 125 = – 125 p = – 450 – 125 – 575 The profit in 2007 was –$575 million.

2 -5 Solving Equations Containing Integers Lesson Quiz Solve each equation. Check your answer. 1. – 8 y = – 800 2. x – 22 = – 18 3. – y 7 =7 100 4 – 49 4. w + 72 = – 21 – 93 5. Last year a phone company had a loss of $25 million. This year the loss is $14 million more last year. What is this years loss? $39 million