1. inequality word problem

The height of a particular ball is given by the formula $h=12t-5t^2$ 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.

2. We want h < 4
but h = 12t-5t^2

so 12t-5t^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)(t-2)=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