https://file.aiquickdraw.com/mathbot/file/1725888469057go78q2vm.jpg

Let's solve the inequality:

\[
-7b + 3(-9b + 5) \geq 10b + 6 + 10
\]

### Step 1: Distribute the 3 on the left-hand side
\[
-7b + 3(-9b) + 3(5) \geq 10b + 16
\]
This simplifies to:
\[
-7b - 27b + 15 \geq 10b + 16
\]

### Step 2: Combine like terms on the left-hand side
\[
-34b + 15 \geq 10b + 16
\]

### Step 3: Move the \(10b\) from the right-hand side to the left-hand side
\[
-34b - 10b + 15 \geq 16
\]
\[
-44b + 15 \geq 16
\]

### Step 4: Subtract 15 from both sides
\[
-44b \geq 16 - 15
\]
\[
-44b \geq 1
\]

### Step 5: Divide both sides by -44, and remember to reverse the inequality sign because we are dividing by a negative number:
\[
b \leq \frac{1}{-44}
\]
\[
b \leq -\frac{1}{44}
\]

### Final Answer:
\[
b \leq -\frac{1}{44}
\]

Would you like further explanation or details on this solution?

Here are some related questions:
1. How do you handle inequalities when multiplying or dividing by negative numbers?
2. What is the importance of combining like terms in an inequality?
3. How can you check the solution to an inequality?
4. What happens to the inequality sign when performing operations on both sides of an inequality?
5. Can you graph the solution \(b \leq -\frac{1}{44}\) on a number line?

**Tip:** Always double-check that you reverse the inequality sign when dividing or multiplying by a negative number.

Learn how to solve the linear inequality -7b + 3(-9b + 5) ≥ 10b + 6 + 10 with a step-by-step explanation. This algebra problem involves distributing, combining like terms, and managing inequalities, suitable for students in Grades 8-10.

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