A H2 math inequalities question

Tanbrenda SG

The question is sketch the graph y= mod (5-x) and then hence using graphical method solve the inequalities of mod [(5/4x^2) - (1/4x)] <= 1 (i.e. less than equal 1)

(the intercept of graph is (0,5) and (5,0)

i solve the inequalities and its mod [(5-x) / (4x^2) ] <= 1 but i do not know how to complete the rest step

please help me thanks !

Mad Hat SG

Hi Tanbrenda

Just multiply both sides of the inequality by | 4x^2 |. You can do this safely since this is a positive quantity, so the inequality sign will remain unchanged. So now you have:

| 5 - x | ≤ | 4x^2 |

If you now draw both the graphs of y = | 5 - x | and y = | 4x^2 | on a single diagram, you should be able to see the answer.