"A pair of consecutive integers has the property that 6 times the smaller is less than 5 times the greater. Find the greatest such integers."

The pair of consecutive integers can be written as x and x+1, where x is integer.

Since x + 1 > x, x is the smaller and x+1 is the larger of the consecutive integers.

6x < 5(x+1)

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click here to see the inequality solved for x

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x < 5

The greatest integer x such that x < 5 is x = 4 thus the pair of consecutive integers is 4 and 5.

"The sum of four consecutive integers decreased by 18 is greater than twice the smallest of four. What are the four smallest such integers?"

The 4 consecutive integers can be written as: x-1, x, x+1, x+2, where x is integer.

(x - 1) + x + (x + 1) + (x + 2) - 18 > 2(x - 1)

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click here to see the inequality solved for x

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x > 7

The smallest integer that is greater than 7 is 8.

The four smallest such integers are 7,8,9 and 10.