Final answer:
To find the interval for x so that {-2x+5}/{7} is between [0,1), we compute two inequalities and find that the solution is -1 < x <= 2.5.
Step-by-step explanation:
To find the interval of all x such that {-2x+5}/{7} is in the interval [0,1), we set up two inequalities based on the definitions of the interval.
First, for the value to be greater than or equal to 0:
-2x + 5 ≥ 0
-2x ≥ -5
x ≤ 5/2
Second, for the value to be less than 1:
-2x + 5 < 7
-2x < 2
x > -1
Combining the two inequalities, we get:
-1 < x ≤ 2.5
This interval represents all the values of x that satisfy the condition set by the original inequality.