To determine which values of [tex]\( z \)[/tex] would not satisfy the inequality [tex]\( 3 - z \geq 7 \)[/tex], we need to isolate [tex]\( z \)[/tex] and find the range of values that do not meet the inequality condition.
### Step-by-Step Solution:
1. Given Inequality:
[tex]\[
3 - z \geq 7
\][/tex]
2. Isolate [tex]\( z \)[/tex]:
Subtract 3 from both sides of the inequality:
[tex]\[
3 - z - 3 \geq 7 - 3
\][/tex]
Simplify the left side:
[tex]\[
-z \geq 4
\][/tex]
3. Isolate [tex]\( z \)[/tex] Further:
Multiply both sides by -1. Remember, multiplying or dividing an inequality by a negative number reverses the inequality symbol:
[tex]\[
z \leq -4
\][/tex]
4. Interpretation:
The solution [tex]\( z \leq -4 \)[/tex] means that [tex]\( z \)[/tex] must be less than or equal to [tex]\(-4\)[/tex] in order to satisfy the inequality [tex]\( 3 - z \geq 7 \)[/tex].
To find the values of [tex]\( z \)[/tex] that do not satisfy the inequality, we look for values of [tex]\( z \)[/tex] that are greater than [tex]\(-4\)[/tex]. Any value of [tex]\( z \)[/tex] in the interval [tex]\( -4 < z \)[/tex] will not satisfy [tex]\( 3 - z \geq 7 \)[/tex].
### Examples of [tex]\( z \)[/tex] values that do not satisfy the inequality:
- [tex]\(-3\)[/tex]
- [tex]\(-2\)[/tex]
- [tex]\(-1\)[/tex]
- [tex]\(0\)[/tex]
- [tex]\(1\)[/tex]
- [tex]\(2\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(4\)[/tex]
- [tex]\(5\)[/tex]
Thus, the values of [tex]\( z \)[/tex] that do not satisfy the inequality [tex]\( 3 - z \geq 7 \)[/tex] are:
[tex]\[
-3, -2, -1, 0, 1, 2, 3, 4, 5
\][/tex]
