Question

How do you solve `4x ^ { 2} - 7x \geq 0`?

Answer 1

`x<=0` and `x>=7/4`

Explanation:

`4x^2-7x >=0`

`x(4x-7) >=0`

Draw the parabola `x(4x-7)` where `x=0` and `x=7/4` are the x-intercepts
graph{4x^2-7x [-10, 10, -5, 5]}

Then, looking at the graph, find what part of the parabola is above or equal to `y=0`

Hopefully you will notice that any value less than or equal `x=0` and any value greater than or equal to `x=7/4`, the parabola is above `y=0`

Hence, the answer is `x<=0` and `x>=7/4`