Given that $$\frac{1}{x} \gt -3$$, which of the following cannot be the value of $$x$$?

Correct.
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__Plug In__ $$x = -\frac{1}{3}$$ into $$\frac{1}{x}$$.
>$$\frac{1}{x} = \frac{1}{-\frac{1}{3}}$$
To simplify the result, change the division to multiplication:
>$$\frac{1}{-\frac{1}{3}} = 1\div (-\frac{1}{3}) = 1\times (-\frac{3}{1}) = -3$$
Since -3 is *not* greater than -3, this answer choice cannot be the value of $$x$$. Also, all other answer choices are eliminated because plugging them into $$\frac{1}{x}$$ results in a value greater than -3.

Incorrect.
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__Plug In__ $$x = -\frac{1}{2}$$ into $$(\frac{1}{x})$$.
>$$\frac{1}{x} = \frac{1}{-\frac{1}{2}}$$
To simplify the result, change the division to multiplication:
>$$\frac{1}{-\frac{1}{2}} = 1 \div (-\frac{2}{1}) = 1 \times (-\frac{2}{1}) = -2$$
Since -2 is greater than -3 (it is more to the right on the number
line and closer to zero), this is a possible value for $$x$$. Eliminate
this answer choice.

Incorrect.
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__Plug In__ $$x = -1$$ into $$\frac{1}{x}$$.
>$$\frac{1}{x} = \frac{1}{-1} = -1$$
Since -1 is greater than -3 (it is more to the right on the number
line and closer to zero), this is a possible value for $$x$$. Eliminate
this answer choice.

Incorrect.
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__Plug In__ $$x= 3$$ into $$\frac{1}{x}$$.
>$$\frac{1}{x} = \frac{1}{3}$$
Since $$\frac{1}{3}$$ is greater than -3 (it is positive), this is a possible value for $$x$$. Eliminate this answer choice.

Incorrect.
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__Plug in__ $$x = -3$$ into $$\frac{1}{x}$$.
>$$\frac{1}{x} = -\frac{1}{3}$$
Since $$-\frac{1}{3}$$ is greater than -3 (it is more to the right on the number
line and closer to zero), this is a possible value for $$x$$. Eliminate
this answer choice.

Default step content.

$$-3$$

$$-1$$

$$-\frac{1}{2}$$

$$-\frac{1}{3}$$

$$3$$