0

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

ABS Math
  • 3
  • 2
    If $x$ is positive, then $|x| = x$, so $-x|x|$ is negative. In short, your solution is correct, and there is some problem with the other solution. For example, $ - 3 \times |3| = -9 < 4$. – Sarvesh Ravichandran Iyer Sep 14 '18 at 03:44

2 Answers2

1

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

If $x>2$

$|x|>2$

$x|x|>4$

$-x|x|<4$

Your solution is actually correct.

Vee Hua Zhi
  • 881
1

The graph for function $$y=-x|x|$$ looks something like thisenter image description here 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!

gen-ℤ ready to perish
  • 6,610
  • I guess the graph was obtained from the Mathway solver . The same solver gave this answer. x>2 or x<-2. There must be something wrong with the Mathway solver. – ABS Math Sep 14 '18 at 04:05
  • 1
    I have edited my answer so you might understand now –  Sep 14 '18 at 04:51
  • I do understand graphs :) What I was talking about is the site(https://www.mathway.com/prealgebra) from which you created the graph. The same site has given the answer for the above question as x>2 or x<-2 when solve for x is selected. That's what confused me in the first place. That was the reason for me putting this question. – ABS Math Sep 14 '18 at 05:00
  • 1
    This graph isn't from mathway.com but from the best graphing calculator Desmos. I would suggest you to graph these functions yourself. And In case you don't know to graph such functions, you can buy a book named "Play with Graphs by Amit m. Aggarwal ". You can search it on Amazon or any other site. I think this the best book to master graphs. –  Sep 14 '18 at 05:24