Challenging Inequality problem 1

Solve the inequality

From G.C, 0.5<x< 2.81, x not equal to 2 (This is the easy part)

Hence solve

This is the HOT (Higher Order Thinking) part.

Method 1

Let f(x) =

Therefore f(x+2) =

f(x+2) is translation of f(x) by 2 units in the negative X direction.

Therefore, the solution is -1.5< x<0.81, x not equal to 0

This solution combines the concept of inequality and transformation of graph.

Method 2

Replace x by x+2.

Therefore 0.5<x+2< 2.81, x+2 not equal to 2

-1.5<x<0.81, x not equal to 0