Solution

Since 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.

\(2^x |?| 3^x^+^1\)

or \(2^x |?| 3* 3^x\)
or \(\frac{2^x}{3^x} |?| 3\)

Let n = -x and since x is negative integer n is a positive integer.

or \((\frac{2}{3})^{-n} |?| 3\)

or \((\frac{3}{2})^n |?| 3\)

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.
_________________

Sandy
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Not edited properly mate.

It should be \(3^{x+1}\) not \(3^x\) + 1

Made me choose the wrong option.

Can someone please tell me why 3^x+1 is the same as 3∗3^x?

Or can just tell me the name of the rule?

I'm sure I should know it, but I don't.

Thanks for your help.