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1212If and , what is the solution to ?

A 3 and 5

1212To solve the equation for x, cross multiply to yield x(x + 2) = 5(2x − 3). Simplifying both sides of the new equation results in . Next, subtract 10x from both sides of the equation and add 15 to both sides of the equation to yield . By factoring the left-hand side, the equation can be rewritten in the form (x − 3)(x − 5) = 0. It follows, therefore, that x = 3 and x = 5.

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