SolutionSince both quantities are algebraic expressions, another way to approach the comparison is to set up a placeholder relationship, denoted by |?|, between the two quantities and then to simplify to see what conclusions you can draw. As you simplify and draw conclusions, keeping in mind that x is a negative integer.
\(2^x vs 3^x^+^1\)
or \(2^x vs 3* 3^x\)
or \(\frac{2^x}{3^x} vs 3\)
Let n = -x and since x is negative integer n is a positive integer.
or \((\frac{2}{3})^{-n} vs 3\)
or \((\frac{3}{2})^n vs 3\)
Now clearly for some values of n Quantity A is bigger (for example n = 1) and other values Quantity B is greater (for example n=3). Hence a relation ship between the two cannot be determined. Option D is correct.
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