
inequality word problem
The height of a particular ball is given by the formula $\displaystyle h=12t5t^2$ where h is the height above the ground in metres and t is the time in seconds.
Form and solve an inequality to find when the height of the ball above the ground is less than 4 metres.
i'm not quite sure how to go about this....

We want h < 4
but h = 12t5t^2
so 12t5t^2 < 4
subtract 4 from both sides gives
12t 5t^2  4 <0
Rearrange as 5t^2 +12t 4 <0
Now consider the graph of 5t^2 +12t 4 (where t is on the X axis)
because this is a quadratic equation with a negative coefficient to the squared term we can say it has an "n" shape
At the axis the graph has a value of zero
5t^2 +12t 4 =0
Factorise
(5t +2)(t2)=0
so t=2/5 or t = 2
This tells us the graph cuts the axis at t=2/5 and t=2
And the graph is negative (5t^2 +12t 4 <0) below the axis ,which because of the "n" shape is to the left of t=2/5 and to the right of t=2
so 2/5 > t > 2
Also t cannot be negative so 0=< t < 2/5 and t>2