1. ## solve inequality equation

Solve inequality equation:

x^2-5x-6<0

2. This is easiest to solve by completing the square.

3. Originally Posted by hoanghai549
Solve inequality equation:

x^2-5x-6<0
Draw a graph of y = x^2 - 5x - 6 and clearly label the x-intercepts. For what values of x is y < 0 ....?

4. Originally Posted by mr fantastic
Draw a graph of y = x^2 - 5x - 6 and clearly label the x-intercepts. For what values of x is y < 0 ....?
Perhaps it's a way as long as you have a quadratic, but how about a higher degree polynomial? Even worse, you're giving an exam and there's nothing no graph it faster, there's where analytically way comes handy.

5. Originally Posted by hoanghai549
Solve inequality equation:

x^2-5x-6<0
An algebraic solution is

$\displaystyle x^2-5x-6<0\Rightarrow\ (x-6)(x+1)<0$

This is negative if the product of the factors gives (-)(+)

If $\displaystyle x<-1,$ both factors are negative

and if $\displaystyle x>6,$ both factors are positive, hence in both cases the product will be positive.

Therefore, one can find from this the valid range of x.

Alternatively

$\displaystyle x^2-5x-6<0\Rightarrow\ x^2-5x<6\Rightarrow\ x(x-5)<6$

$\displaystyle x>6\Rightarrow\ (+)(+)>6$

$\displaystyle x<-1\Rightarrow\ (-)(-)>6$

Again, the range of x can be deduced.