Let's solve the equation:

\[
-8x + 23 - 22x + 9 = 182
\]

### Step 1: Combine like terms
Group the \(x\)-terms together and the constant terms together:

\[
(-8x - 22x) + (23 + 9) = 182
\]

This simplifies to:

\[
-30x + 32 = 182
\]

### Step 2: Isolate the variable term
Subtract 32 from both sides of the equation:

\[
-30x = 182 - 32
\]

\[
-30x = 150
\]

### Step 3: Solve for \(x\)
Divide both sides by \(-30\):

\[
x = \frac{150}{-30}
\]

\[
x = -5
\]

So, the solution to the equation is:

\[
x = -5
\]

Would you like further details or have any questions?

Here are some related questions to explore:
1. How would you solve \(5x + 10 = 3x + 50\)?
2. What happens when you multiply both sides of an equation by a negative number?
3. How do you check if your solution to an equation is correct?
4. What are some common mistakes to avoid when solving linear equations?
5. Can you solve an equation with variables on both sides of the equal sign?

**Tip**: Always simplify the equation step by step, combining like terms first to avoid errors!

Learn how to solve the linear equation -8x + 23 - 22x + 9 = 182 with a step-by-step guide. This problem involves algebraic concepts like combining like terms and isolating variables, suitable for students in Grades 8-10.

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