The three consecutive negative integers are -5 , -4 , -3
Step-by-step explanation:
Consecutive numbers are numbers that follow each other in order.
They have a difference of 1 between every two numbers
Examples:
- 2 , 3 , 4, .......
- -5 , -4 , -3 , .......
- n , n + 1 , n + 2 , ........
Assume that the smallest negative number is -n
∵ There are three negative consecutive numbers
∵ The smallest one = -n
∴ The three numbers are (-n) , (-n + 1) , (-n + 2)
∵ The largest number is (-n + 2)
∵ Six times the largest is equal to the twice sum of the two smaller
integers
- Multiply (-n + 2) by 6 and multiply the the sum of (-n) and (-n + 1) by 2
∴ 6(-n + 2) = 2[(-n) + (-n + 1)]
- Simplify the equation
∵ 6(-n) + 6(2) = 2[-2n + 1]
∴ -6n + 12 = 2(-2n) + 2(1)
∴ -6n + 12 = -4n + 2
- Subtract 12 from both sides
∴ -6n = -4n - 10
- Add 4n to both sides
∴ -2n = -10
- Divide both sides by -2
∴ n = 5
∵ The numbers are (-n) , (-n + 1) , (-n + 2)
∴ The numbers are (-5) , (-5 + 1) , (-5 + 2)
∴ The numbers are (-5) , (-4) , (-3)
The three consecutive negative integers are -5 , -4 , -3
Learn more:
You can learn more about consecutive numbers in brainly.com/question/5496711
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