Solve `|x^(2)-1|+|x^(2)-4|lt6` graphically.

Explanation

We have `|x^(2)-1|+|x^(2)-4|lt6`
`because|x^(2)-1|lt6-|x^(2)-4|`
Let us draw the graphs of `y=|x^(2)-1|andy=6-|x^(2)-4|`.
The graph of `y=|x^(2)-1|` is as follows.

Graph of `y=|x^(2)-1|` is as follows.

Graph of `y=|x^(2)-4|` is as follows.

Garph of `y=|x^(2)-4|` is as follows
Graph of `y=6-|x^(2)-4|` is as follows.

Graphs of `y=|x^(2)-1|andy=6-|x^(2)-4|` are as shown in the following figure.

For `|x^(2)-1|lt6-|x^(2)-4|,` the graph of `y=|x^(2)-1|` lies below the graph of `y=6-|x^(2)-4|`, the values of x lying between points A and B.
Solving `y=|x^(2)-1|andy=6-|x^(2)-4|` for points of intersection, we have `x^(2)-1=6-(x^(2)-4)orx^(2)=11//2`.
From the graph, the solution is `x in(-sqrt((11)/(2)),sqrt((11)/(2)))`.