Step-by-step explanation:
The problem asks to find the values "b" and "c" in a way that
the solutions of the equation |x - b| = c are x= 1/2 and x= -1/3.
It means that "b" is the center of the segment [-[tex]\frac{1}{3} ,\frac{1}{2}[/tex]].
This segment has the length [tex]\frac{1}{2} - ( - \frac{1}{3} = \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}[/tex] Hence, the half of this length is [tex]\frac{5}{12}[/tex].
Therefore, the center of the segment is [tex]\frac{1}{2} - \frac{5}{12} = \frac{6}{12} - \frac{5}{12} = \frac{1}{12}[/tex]
Thus the value of "b" is found: it is b = [tex]\frac{1}{12}[/tex].
Then the value of "c" is c =[tex]\frac{1}{2} - \frac{1}{12} = \frac{5}{12}[/tex].
