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# Inequalities: Overview

Given that $$\frac{1}{x} \gt -3$$, which of the following cannot be the value of $$x$$?
Correct. [[Snippet]] __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. [[Snippet]] __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. [[Snippet]] __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. [[Snippet]] __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. [[Snippet]] __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.
$$-3$$
$$-1$$
$$-\frac{1}{2}$$
$$-\frac{1}{3}$$
$$3$$