Question 6470
in learning maths, you have to understand what you are doing..not just the mechanics of working with inequalities, which you are OK with , but the understanding of what (4x-3)(x+7)<=0 is.


This is a quadratic equation, as such it is a u-shape. This u-shape, when plotted, crosses the x-axis at 2 points called the roots/solutions. 


For a u-shape:
the curve is GREATER than zero, to the left of the lefthand root and also to the right of the righthand root.
the curve is LESS than zero, between the 2 roots. 


So, understading this, you need to find your roots first and then "picture them" on a graph and the answer will be the ragion between them. What you have done is ASSUME something about your roots: you have assumed that both brackets are <=0..it does not say that, it says that BOTH BRACKETS MULTIPLIED TOGETHER is <=0 :-)


OK... to find the roots: --> (4x-3)(x+7)=0


so, either 4x-3=0 OR x+7=0


so x = 3/4 OR x=-7


so, where is the curve negative Mike? Visualise the curve: it is negative between -7 and 3/4. That is your answer.


jon.