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Find the lesser of two consecutive positive even integers whose product is 168.
Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a key word for multiplication, the equation is x(x + 2) = 168. Multiply using the distributive property on the left side of the equation: x2 + 2x = 168. Put the equation in standard form and set it equal to zero: x2 + 2x - 168 = 0. Factor the trinomial: (x - 12)(x + 14) = 0. Set every factor equal to zero and solve: x - 12 = 0 or x + 14 = 0; x = 12 or x = -14. Because you are seems for a positive integer, reject the x-value of -14. Thus, the lesser positive integer would be 12.
About Zeros in the Denominator of Rational Expressions One thing that you must be careful about when working with rational expressions is that the denominator can never be zero
state tha different types of models used in operations research.
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