Question

Find the solution of the inequality x^2-4x>5 algebraically.

Answer 1

x^2-4x-5>0
(x-5)(x+1)>0

Answer 2

\[x^2 - 4x - 5 > 0\]
\[=> (x+1)(x-5) > 0\]

Now draw the no. line and plot the critical points, which are "-1" and "+5" in this case, and check the intervals for which the functional value is negative or positive.


The two rays below the no. line emaninating from -1 and 5 represent the allowed values of 'x'.
The hollow circles below '-1' and '5' both represent the fact that x cannot take the values '-1' and '5' itself, because at those points the function gets reduced to zero, and what we need here is the function to be "greater" than zero.

so, the solution would be:

\[x\[x \epsilon(- \infty,-1) U (5, \infty)\]