Here are some challenges to try:
Find two expressions so that one is bigger whenever n<5 and the other is bigger whenever n>5.
To solve this, i took a positive coefficient of x and added it to a constant, to give a larger coefficient of x. This gives us the equation:
2x + n = 3x
Now I substituted x to be 5, as only then would the two equations be equal to each other.
2(5) + n = 3(5)
10 + n = 15
n = 5
Therefore, the two expressions are:
2x + 5
3x
I then plotted this on a graph, and inferred that:
When x<5, the line 2x+5 is greater than 3x
When x>5, the line 3x is greater than 2x+5
Find three expressions so that the first is biggest whenever n<0, the second is biggest whenever n is between 0 and 4, and the third is biggest whenever n>4.
Again, I used the same approach, and formed three lines of myself. However this time, one of the lines needed x to have a negative coefficient, as when x is negative, the line has to be the biggest. The line I chose was -2x.
For the remaining two lines, I again used a positive coefficient of x and added it to a constant, to give a larger coefficient of x. This gives us the equation:
3x + n = 4x
3(4) + n = 4(4)
12 + n = 16
n = 4
Therefore, the three equations are:
3x+4
4x
-2x
I then plotted this on a graph, and inferred that:
When x<0, the line -2x is the biggest
When x<4, the line 3x+4 is the biggest
When x>4, 4x is the biggest