MHB Overcoming Struggles to Addressing Inequalities Step by Step

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The discussion focuses on the challenges of understanding inequalities in mathematical functions. Participants express a desire for a step-by-step approach to grasp these concepts better. The conversation highlights the significance of the function f(x) in determining the values above, on, or below the x-axis. Clarifications are sought regarding the specific inequalities related to a particular item, emphasizing the relationship between f(x) and y values. Overall, the thread aims to provide guidance on overcoming struggles with mathematical inequalities.
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I’m overall struggling. Not liking the inequalities. Any step by step would be awesome
 

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$f(x) > 0$ is any part of the graph that is above the x-axis

$f(x) = 0$ is any part of the graph that crosses or touches the x-axis

$f(x) < 0$ is any part of the graph below the x-axis
 
Beer soaked query follows.
Seka88 said:
I’m overall struggling. Not liking the inequalities. Any step by step would be awesome
D97F9FC9-ABA4-4A78-956C-B889286E4D18.jpeg

Is there a specific inequality behind item #5?
 
Do you not understand that in "y= f(x)" any value of f is a "y" value? f(x)= 0 means y= 0 so that is a point on the x- axis. That is what goes into the first two blanks. For the other two we need to know how "f(x)" is defined here.
 
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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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