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

1 Answer
Mar 11, 2016

Answer:

#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

Drawn with Graphmatica

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