Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8

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2 Bell Ringer Solve each equation. Show you work. the solution = 7 + m 8 = -7 + m = m 15 = m 8 = -7 + m 8 = = 8

3 Answers to Homework Worksheet 2-1

4 Today s Objectives Solving Two Step Equations

5 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Our first two step equation We don t see a multiplication sign so we assume it is multiplication 2x + 5 = x + 0 = 10 2x = 10 2 x = 5 2 2x + 5 = 15 2(5) + 5 = = = 15 The process is basically the same as a one step Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 5 s cancel each other out, by adding/subtracting to 0 (zero) 15 minus 5 is 10 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The 2 s cancel each other out, by dividing to 1 10 divided by 2 is 5 The solution is x = 5 the solution

6 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation We don t see a multiplication sign so we assume it is multiplication 3x - 1 = x + 0 = 21 3x = 21 3 x = 7 3 3x - 1 = 20 3(7) - 1 = = = 20 Identify the variable, it is x Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 1 s cancel each other out, by adding/subtracting to 0 (zero) 20 plus 1 is 21 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The 3 s cancel each other out, by dividing to 1 21 divided by 3 is 7 The solution is x = 7 the solution

7 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation We don t see a multiplication sign so we assume it is multiplication -3b - 5 = b + 0 = 18-3b = b = -6-3b - 5 = 13-3(-6) - 5 = = = 13 Identify the variable, it is b Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 5 s cancel each other out, by adding/subtracting to 0 (zero) 13 plus 5 is 18 Notice the operation of multiplication, so we do the opposite to both sides Now divide from both sides The -3 s cancel each other out, by dividing to 1 18 divided by -3 is -6 The solution is b = -6 the solution

8 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division n - 3 = n - 3 = = 7 2 n + 0 = 10 2 (2) n = 10 (2) = 7 7 = 7 n = 20 Identify the variable, it is n Notice the operation of subtraction, so we do the opposite to both sides Now add to both sides The 3 s cancel each other out, by adding/subtracting to 0 (zero) 7 plus 3 is 10 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The 2 s cancel each other out, by multiplying to 1 10 multiplied by 2 is 20 The solution is n = 20 the solution

9 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division x + 9 = x + 0 = 4 7 (7) x = 4 (7) 7 x = 28 x + 9 = = = = 13 Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 9 s cancel each other out, by adding/subtracting to 0 (zero) 13 minus 9 is 4 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The 7 s cancel each other out, by multiplying to 1 4 multiplied by 7 is 28 The solution is x = 28 the solution

10 When we solve two step equations, we do all of our adding and subtracting first. Then we multiply or divide. Solve: Another two step equation, but with division x + 3 = x + 0 = -8-4 (-4) x = -8 (-4) -4 x + 3 = = = -5-5 = -5 x = 32 Identify the variable, it is x Notice the operation of addition, so we do the opposite to both sides Now subtract from both sides The 3 s cancel each other out, by adding/subtracting to 0 (zero) -5 minus -3 is -8 Notice the operation of division, so we do the opposite to both sides Now multiply both sides The -4 s cancel each other out, by multiplying to 1-8 multiplied by -7 is 32 The solution is x = 32 the solution

11 Quick Review x + 6 = x + 0 = -2-2 (-2) x = -2 (-2) -2 x = 4 x + 6 = = = 4 4 = 4 14j - 7 = j + 0 = 91 14j = j = 7 14j - 7 = 91 14(7) - 7 = = = a - 3 = a + 0 = 8 240a = a = a - 3 = = = 5 5 = 5

12 x + 7 = x + 0 = 4-4 (-4) x = 4 (-4) -4 x = -16 x + 7 = = = = 11 Quick Review Show your work as you solve the following equations. Then check each. 1. x + 7 = b - 50 = h - 8 = b - 50 = b = b = 22 3b - 50 = 16 3(22) - 50 = = = 16 7h - 8 = h = h = 5 7h - 8 = 27 7(5) - 8 = = = 27

13 z - 5 = (3) z = 2 (3) 3 z = 6 z - 5 = = = -3-3 = -3 Quick Review Show your work as you solve the following equations. Then check each. 4. z - 5 = m - 13 = k + 12 = m - 13 = m = m = 9 6m - 13 = 41 6(9) - 13 = = = 41-4k + 12 = k = k = 5-4k + 12 = -20-4(5) + 12 = = = -20

14 v - 12 = (-9) v = 21 (-9) -9 v = -189 v - 12 = = = 9 9 = 9 Quick Review Show your work as you solve the following equations. Then check each. 7. v - 12 = s - 7 = p + 7 = s - 7 = s = s = 22 2s - 7 = 37 2(22) - 7 = = = 37-9p + 7 = p = p = -11-9p + 7 = 106-9(-11) + 7 = = = 106

15 Quick Review Show your work as you solve the following equations. Then check each. 10. g + 9 = 20-3 g + 9 = (-3) g = 11 (-3) -3 g = -33 g + 9 = = = = 20

16 SHOWING YOUR WORK 10. g + 9 = 20-3 g + 9 = (-3) g = 11 (-3) -3 g = -33 g + 9 = = = = 20

17 Assignment Worksheet 7-3 A

18 Answers to Homework Worksheet 7-3 A