Find the truth set of 1-x<6, where x (-10,-9,-8,___,0)

To find the truth set of 1-x < 6 for x in the set (-10, -9, -8, ..., 0), we need to substitute each value of x into the inequality and determine if it is true or false.

1. For x = -10:
1 - (-10) < 6
1 + 10 < 6
11 < 6
False

2. For x = -9:
1 - (-9) < 6
1 + 9 < 6
10 < 6
False

3. For x = -8:
1 - (-8) < 6
1 + 8 < 6
9 < 6
False

4. For x = -7:
1 - (-7) < 6
1 + 7 < 6
8 < 6
False

5. For x = -6:
1 - (-6) < 6
1 + 6 < 6
7 < 6
False

6. For x = -5:
1 - (-5) < 6
1 + 5 < 6
6 < 6
False

7. For x = -4:
1 - (-4) < 6
1 + 4 < 6
5 < 6
True

8. For x = -3, -2, -1, or 0:
1 - x < 6
1 - (-3, -2, -1, or 0) < 6
1 + 3, 2, 1, or 0 < 6
4, 3, 2, or 1 < 6
True

Therefore, the truth set for the inequality 1-x < 6 for x in the set (-10, -9, -8, ..., 0) is { -4, -3, -2, -1, 0 }.