Question

PLEASE HELP ASAP

Answer 1

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 [-$\frac{1}{3} ,\frac{1}{2}$].

This segment has the length $\frac{1}{2} - ( - \frac{1}{3} = \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$  Hence, the half of this length is $\frac{5}{12}$.

Therefore, the center of the segment is $\frac{1}{2} - \frac{5}{12} = \frac{6}{12} - \frac{5}{12} = \frac{1}{12}$

Thus the value of "b" is found: it is b = $\frac{1}{12}$.

Then the value of "c" is  c =$\frac{1}{2} - \frac{1}{12} = \frac{5}{12}$.