To determine which of the given values are solutions to the inequality [tex]\(-9 \geq -9 - 6x\)[/tex], let's solve it step-by-step.
First, isolate [tex]\(x\)[/tex] in the inequality:
[tex]\[ -9 \geq -9 - 6x \][/tex]
Add 9 to both sides of the inequality to simplify:
[tex]\[ -9 + 9 \geq -9 + 9 - 6x \][/tex]
[tex]\[ 0 \geq -6x \][/tex]
Now, divide both sides by -6. Remember, when dividing or multiplying an inequality by a negative number, we need to reverse the inequality sign:
[tex]\[ 0 \leq x \][/tex]
This simplifies to:
[tex]\[ x \geq 0 \][/tex]
Now, we will check the given values to see which ones satisfy [tex]\( x \geq 0 \)[/tex]:
I. [tex]\( x = -8 \)[/tex]
[tex]\[ -8 \geq 0 \][/tex]
This is false, so -8 is not a solution.
II. [tex]\( x = 2 \)[/tex]
[tex]\[ 2 \geq 0 \][/tex]
This is true, so 2 is a solution.
III. [tex]\( x = 0 \)[/tex]
[tex]\[ 0 \geq 0 \][/tex]
This is true, so 0 is a solution.
Thus, the values that are solutions to the inequality [tex]\(-9 \geq -9 - 6x\)[/tex] are:
[tex]\[ I. -8 \ \text{(no)} \][/tex]
[tex]\[ II. 2 \ \text{(yes)} \][/tex]
[tex]\[ III. 0 \ \text{(yes)} \][/tex]
Therefore, the values that are solutions are:
[tex]\[ \boxed{2 \text{ and } 0} \][/tex]
