Determine which one of the following values of x is not a soluton of the inequality 0<x+5/6<2.
0 < x + 5 / 6
0 - 5 / 6 < x
- 5 / 6 < x
x > - 5 / 6
x + 5 / 6 < 2
x < 2 - 5 / 6
x < 12 / 6 - 5 / 6
x < 7 / 6
All values of x betwen - 5 / 6 and 7 / 6 is a soluton of the inequality.
Remark:
-5 / 6 and 7 / 6 is not a soluton of the inequality.
To determine which value of x is not a solution of the inequality 0 < x + 5/6 < 2, we need to solve the inequality and verify if each value satisfies the inequality.
Step 1: Subtract 5/6 from all parts of the inequality:
0 - 5/6 < x + 5/6 - 5/6 < 2 - 5/6
-5/6 < x < 7/6
Step 2: Now we can check each value and see if it satisfies the inequality.
a) Let's check x = -1
-5/6 < -1 < 7/6
-5/6 < -1 is true, but (-1) < 7/6 is also true.
Therefore, x = -1 satisfies the inequality.
b) Let's check x = 0
-5/6 < 0 < 7/6
-5/6 < 0 is true, and 0 < 7/6 is also true.
Therefore, x = 0 satisfies the inequality.
c) Let's check x = 1
-5/6 < 1 < 7/6
-5/6 < 1 is true, but 1 < 7/6 is not true.
Therefore, x = 1 does not satisfy the inequality.
d) Let's check x = 2
-5/6 < 2 < 7/6
-5/6 < 2 is true, and 2 < 7/6 is also true.
Therefore, x = 2 satisfies the inequality.
From the above analysis, we can see that x = 1 does not satisfy the inequality 0 < x + 5/6 < 2.