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First, translate the words into expressions:

"Two less than one-sixth [of] a certain number..."

((1/6) * X) - 2

"is"

=

"1 more than one-fourth that number"

((1/4) * X) + 1

so

((1/6) * X) - 2 = ((1/4) * X) + 1

((1/6) * X) = ((1/4) * X) + 3

X = ((6/4) * X) + 18

(1 - (6/4)) * X = 18

- (1/2) * X = 18

X = - 36

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