What is the range of $x$ satisfying the inequality $-x|x| > 4$ where $x$ is an integer?

Question

The range according to me is x<-2. But I got to know that x>2 is also a possible solution. How can that be correct?

P.S. I know that this is a simple question. But I couldn't find any existing question in the forum related to this. If there exists one, please point me that way.

Edit:

Mathway solver response

Answer 1

Note that $x>2$ is not a solution.

If $x>2$

$|x|>2$

$x|x|>4$

$-x|x|<4$

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Your solution is actually correct.

Answer 2

The graph for function $$y=-x|x|$$ looks something like this Here the red line represents $y=-x|x|$ and blue line represents $y=4$.

Therefore the integer values of $x$ such that $$-x|x|>4$$ are $x=-3,-4,-5,.....$

Edit:-

The horizontal line on which the points $0,1,2...etc$ are marked is called the x-axis. Similarly the vertical line on which the points $0,1,2...etc$ are marked is called the y-axis. The red line here is the graph of $y=-x|x|$. From the graph you can see as one moves towards $-ve$ x-axis, value of $y$ increases and $x$ decreases. As we approach $x=-2$, $y$ equals $4$. And as we move further towards $-ve$ x-axis, value of $y$ i.e. $-x|x|$ increases. Therefore the integer solutions of $x$ are $-3,-4,-5...$.

Hope this helps!