If $$22 ≥ 6 - 2b ≥ -4$$, which of the following is the largest possible value of $$b$$?

Correct.
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First, isolate the variable as in one-variable linear equations. In this case, subtract $$6$$ from each part of the inequality.
>$$22-6 ≥ 6 - 2b-6 ≥ -4-6$$
>$$16 ≥ -2b ≥ -10$$
Divide each part of the inequality by $$-2$$. You need to flip the inequality sign when you do that.
>$$\displaystyle \frac{16}{-2} ≤ \frac{-2b}{-2} ≤ \frac{-10}{-2}$$
>$$-8 ≤ b ≤ 5$$
Based on this, the largest possible value of $$b$$ is $$5$$. Hence, this is the correct answer.

Incorrect.
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Carefully check your work.

Incorrect.
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You might have gotten this answer if you made a sign error when solving for $$b$$.

Incorrect.

Did you forget to flip the sign of the inequality when dividing by $$-2$$? [[Snippet]]Incorrect.
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Check your calculations carefully.

$$-8$$

$$-5$$

$$3$$

$$5$$

$$13$$