We have `y= |2x+3|+ |2x-3|`
`" "={{:(4x",",, xge(3)/(2)), (6",",,-(3)/(2)lt x lt (3)/(2)), (-4x",",, x le -(3)/(2)):}`
The graph of the function is as shown in the following figure.
`y= ax + 6` is a line passing through `(0, 6)`.
From the graph, it is obvious that if `a=0`, we have infinite solutions in `[-(3)/(2), (3)/(2)]`.
If `0 lt a lt 4 or -4 lt a lt 0`, two solutions.
If `a=4 or -4`, we have `x=0` as the only solution.
