https://file.aiquickdraw.com/mathbot/file/1726096928144vrtax9sa.jpg

The equation provided in the image is:

\[
25 - 31 = 3(x + 8) - 15x - 6
\]

Let's solve this step by step.

### Step 1: Simplify both sides
On the left-hand side, we simplify \( 25 - 31 \):

\[
25 - 31 = -6
\]

Now the equation becomes:

\[
-6 = 3(x + 8) - 15x - 6
\]

### Step 2: Distribute the \(3\) on the right-hand side
Expand \( 3(x + 8) \):

\[
3(x + 8) = 3x + 24
\]

So the equation becomes:

\[
-6 = 3x + 24 - 15x - 6
\]

### Step 3: Combine like terms on the right-hand side
First, combine the constants \( 24 - 6 \):

\[
24 - 6 = 18
\]

Next, combine the \( x \)-terms: \( 3x - 15x \):

\[
3x - 15x = -12x
\]

Now the equation is:

\[
-6 = -12x + 18
\]

### Step 4: Isolate the variable term
Subtract 18 from both sides:

\[
-6 - 18 = -12x
\]

Simplifying:

\[
-24 = -12x
\]

### Step 5: Solve for \(x\)
Divide both sides by \(-12\):

\[
x = \frac{-24}{-12} = 2
\]

### Final Solution:
\[
x = 2
\]

Do you need any further details or clarifications?

Here are five related questions to expand your understanding:
1. What happens if the equation contains fractions? How would you solve it?
2. Can you create a similar equation and solve it?
3. How does distributing affect solving multi-step equations?
4. What is the importance of combining like terms in equations?
5. What would be the solution if we change the signs in front of some terms?

**Tip:** Always simplify the equation step by step and check your final solution by substituting it back into the original equation.

Learn how to solve the linear equation 25 - 31 = 3(x + 8) - 15x - 6 using the distributive property and combining like terms. Follow the step-by-step breakdown to isolate the variable and find the solution. Suitable for students in Grades 7-9.

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