Question 12(e) | BetaMath

Question 12(e)

The diagram shows the graph of $\displaystyle y=\frac1{|x-5|}$ .

Graph of the equation

For what values of $x$ is $\displaystyle \frac{x}{6} > \frac1{|x-5|}$

Solution

We know that the line $\displaystyle y=\frac{x}{6}$ will pass through the origin and will have a positive gradient.

From inspection of the graph, it will pass through a point of the right branch of the hyperbola at some point $(x_0, y_0)$ and for all $x>x_0$ the statement $\displaystyle \frac{x}{6} > \frac1{|x-5|}$ will be true.

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