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# Inequalities with a square watch

1. I just want to quickly check something.

If you have an inequality such as:
x2 > 16

Root 16 is + or - 4, right?

Therefore, I, at first thought eh answer would be:
x > 4
x > -4

and hence the only real solution is:
x > -4

But, the mark scheme said that the answer would be #
x > 4 and x < -4

Does this mean that for the negative one, we have to switch the inequality over, just like we do if me multiple the expression by -1?
2. In response to the mark scheme, if x(squared) has to be bigger than 16 then the numbers after 4 (5,6,7,8....) will satisfy this inequality. This is why 'x' must be bigger than 4 and less than -4 so the numbers beyond these limits can satisfy the inequality. So if x=-1 was put it, it would not satisfy the equation and in order for it to do so the sign > would have to be switched <.
3. re-arrange the inequality as:

another way to look at this is - it`s saying: where is the y value positive?

think about the plot of

this is symmetrical about the y-axis, and has a minimum y value of -16, and roots at +4 and -4. So it is concave up from y=-16, and so negative in the range AND POSITIVE EVERWHERE ELSE. (x>4, x<-4)
Attached Images

4. (X^2) > 16
(x^2) - 16 > 0

draw a graph of x squared -16, it will cross the x-axis at 4 and -4. now you want all the places where the graph is bigger than zero, so basically all the places above the x-axis. so the line is above the x-axis when x is less than -4, and when x is greater than 4, but not anywhere between -4 and 4

hence -4>x and 4<x

can you see that on the graph, let me know

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