1.) Three consecutive odd integers

Let 'x' be the first number

'x+2' be the second number

'x+4' be the third number

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-Three times the largest is seven times the smallest

7x = 3(x+4)

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Distribute 3 to the quantity (x+4)

7x = 3x + 12

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Transpose 3x to the left side of the equation

7x - 3x = 12

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Combine like terms

4x = 12

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Divide the whole equation with 4

x = 3

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__x = 3__

x + 2 = 3 + 2

__x + 2 = 5__

x + 4 = 3 + 4

__x + 4 = 7__

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Therefore the three consecutive odd integers are **3, 5, 7.**

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2.) Two numbers are consecutive even

Let 'x' be the first number

'x+2' be the second number

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-If twice the smaller is 18 more than the larger

2x = (x+2) + 18

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Remove parenthesis

2x = x + 2 + 18

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Transpose x to the left side of the equation

2x - x = 2 + 18

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Combine like terms

x = 20

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__x = 20__

x + 2 = 20 + 2

__x + 2 = 22__

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Therefore the two consecutive even numbers are **20, 22.**