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## Consecutive Numbers

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**are numbers in counting order**Examples -3, -2, -1, 0, 1, 2, 3 Consecutive Integers ---|-----|------|-----|------|-----|-----|-----|-----|-----|-----|-----|-----|-----|--- -2 -1 0 1 2 3 4 5 6 7 8 9 10 11**When counting CONSECUTIVE integers, You will…**Add by 1’s Ex + 1, + 2, + 3 When counting CONSECUTIVE ODD OR EVEN integers, you will … Add by 2’s Ex + 2, + 4, + 6, + 8 ---|-----|------|-----|------|-----|-----|-----|-----|-----|-----|-----|-----|-----|--- -2 -1 0 1 2 3 4 5 6 7 8 9 10 11**Examples**• The sum of two consecutive integers is 17. Find the two numbers. • x + 0 » represents 1st number • x + 1 » represents 2nd number • 2x + 1 = 17 add 1st and 2nd number together and set equal to 17. Solve. • -1 -1 • 2x = 16 • 2 2 • X=8 Now x + 0 becomes 8 + 0 which is 8 Now x +1 becomes 8 + 1 which is 9 Check 8 + 9 = 17**Examples**2) The sum of threeconsecutive integers is 129. Find the three numbers. x + 0 » represents 1st number x + 1 » represents 2nd number x + 2 » represents 3rd number 3x + 3 = 129 add 1st, 2nd & 3rd number together and set equal to 129. Solve. -3 -3 3x = 126 3 3 X=42 Now x + 0 becomes 42 + 0 which is 42 Now x +1 becomes 42 + 1 which is 43 Now x + 2 becomes 42 + 2 which is 44 Check 42 + 43 + 44 =129**Examples**3) The sum of four consecutive integers is -334. Find the four numbers. x + 0 » represents 1st number x + 1 » represents 2nd number x + 2 » represents 3rd number x + 3 » represents 4th number 4x + 6 = -334 add 1st, 2nd , 3rd & 4th number together and set equal to -334. Solve. -6 -6 4x = -340 4 4 X=-85 Now x + 0 becomes -85 + 0 which is -85 Now x +1 becomes -85 + 1 which is -84 Now x + 2 becomes -85 + 2 which is -83 Now x + 3 becomes -85 + 3 which is -82 Check -85 + -84 + -83 + -82 = -334**Examples**4) The sum of threeconsecutive integers is 105. Find the three numbers. x + 0 » represents 1st number x + 1 » represents 2nd number x + 2 » represents 3rd number 3x + 3 = 105 add 1st, 2nd & 3rd number together and set equal to 105. Solve. -3 -3 3x = 102 3 3 X=34 Now x + 0 becomes 34 + 0 which is 34 Now x +1 becomes 34 + 1 which is 35 Now x + 2 becomes 34 + 2 which is 36 Check 34 + 35 + 36 = 105**Examples**5) The sum of threeconsecutive even integers is 396. Find the three numbers. x + 0 » represents 1st number x + 2 » represents 2nd number x + 4 » represents 3rd number 3x + 6 = 396 add 1st, 2nd & 3rd number together and set equal to 396. Solve. -6 -6 3x = 390 3 3 X=130 Now x + 0 becomes 130 + 0 which is 130 Now x +2 becomes 130 + 2 which is 132 Now x + 4 becomes 130 + 4 which is 134 Check 130 + 132 + 134 = 396**Examples**6) The sum of fourconsecutive even integers is 138. Find the four numbers. x + 0 » represents 1st number x + 2 » represents 2nd number x + 4 » represents 3rd number x + 6 » represents 4th number 4x + 12 = 138 add these number together and set equal to 138. Solve. -12 -12 4x = 126 4 4 X=31.5 No solution: Must be whole number**Examples**7) The sum of threeconsecutive odd integers is 285. Find the three numbers. x + 0 » represents 1st number x + 2 » represents 2nd number x + 4 » represents 3rd number 3x + 6 = 285 add 1st, 2nd & 3rd number together and set equal to 285. Solve. -6 -6 3x = 279 3 3 X=93 Now x + 0 becomes 93 + 0 which is 93 Now x + 2 becomes 93 + 2 which is 95 Now x + 4 becomes 93 + 4 which is 97 Check 93 + 95 + 97 = 285**Examples**8) The sum of fourconsecutive odd integers is 0. Find the four numbers. x + 0 » represents 1st number x + 2 » represents 2nd number x + 4 » represents 3rd number x + 6 » represents 4th number 4x + 12 = 0 add these number together and set equal to 0. Solve. -12 -12 4x = -12 4 4 X=-3 Now x + 0 becomes -3 + 0 which is -3 Now x + 2 becomes -3 + 2 which is -1 Now x + 4 becomes -3 + 4 which is 1 Now x + 6 becomes -3 + 6 which is 3 Check -3 + -1 + 1 + 3 = 0**The perimeter of a rectangle**with sides of length x and 2x - 1 The perimeter of a rectangle is the sum of the lengths of the sides x In words: 2 sides + 2 sides 2 sides 2 sides 2x - 1 Translate: 2(x) + 2(2x-1) Then: 2x + 4x-2 6x - 2 simplify