Question

How do you graph and solve `3/2 abs( 2x-5 ) -2= 7`?

Answer 1

`x=-1/2` or `x=11/2`

Explanation:

First thing to do would be to simplify things a little.

`3/2 abs(2x-5) -2 = 7 iff 3/2 abs(2x-5) = 9 iff abs(2x-5) = 6`

Next we draw a graph of `y_1 = abs(2x-5)` and `y_2 = 6` to see where they intersect. The point of intersection corresponds to a solution.

To graph `y_1 = abs(2x-5)`, we know that minimum occurs when `y_1 = 0` at `x = 5/2`. Therefore, the graph is symmetrical about the line `x = 2.5`. The graph is a V-shape.
graph{abs(2x-5) [-7, 12, -3, 7]}
The graph `y_2 = 6` is just a horizontal line at the height `y=6`.
graph{6+0x [-16.5, 21.5, -8, 12]}
When graphed together, they look like

They intersect at `(-0.5,6)` and `(5.5,6)`.