Solve for b.–2–4b≤–6b–18Write your answer with b first, followed by an inequality symbol.

1. Break Down the Problem

We need to solve the inequality: $-2 - 4b \leq -6b - 18$

2. Relevant Concepts

To solve this inequality, we will combine like terms and isolate $b$.

3. Analysis and Detail

We start by rewriting the inequality:

1. Combine $b$ terms on one side: $-4b + 6b \leq -18 + 2$
2. Simplify both sides: $2b \leq -16$
3. Now, we divide both sides by 2: $b \leq -8$

4. Verify and Summarize

We have determined that: $b \leq -8$ To verify, if we substitute $b = -8$ back into the original inequality: $-2 - 4(-8) \leq -6(-8) - 18$ Calculating gives: $-2 + 32 \leq 48 - 18 \Rightarrow 30 \leq 30$ This is true.

Final Answer

$b \leq -8$