This problem is done by combining numbers with shapes. Draw (2x- 1) in rectangular coordinate system first? And draw an axe? Image, want to draw an axe? You must first determine the positive and negative of a. As can be seen from the figure, when a takes a negative value, ax? Is the mirror always (2x- 1)? Next, when a=0, two functions are equal except x= 1/2. In which case is ax? Is the mirror always (2x- 1)? Below, so a>0, the title says "There are exactly three integers in the solution set", so we can know from the image that when there are two special values x=3 and x=4, it is the interval at both ends of the integer value that can be taken, and when x=3, (2x- 1)? =25，ax？ =25，a*3？ =25, at this time a=25/9. If this value is included, there are only two integer solutions, so this is an open interval. When x=4, (2x- 1)? =49，ax？ =49，a*4？ =49, a=49/ 16, and this value can be obtained here, so the value range of a is

(25/9,49/ 16]