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

1 Answer
Bio
Mar 11, 2016

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).

Related questions
See all questions in Absolute Value Equations
Impact of this question
1652 views around the world
You can reuse this answer
Creative Commons License