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The equation given is:

\[
a = bx + cx + d
\]

We need to solve for \( x \). Let's break it down step-by-step.

### Step 1: Combine like terms involving \( x \).
The terms \( bx \) and \( cx \) both have \( x \), so we can factor \( x \) from them:

\[
a = x(b + c) + d
\]

### Step 2: Isolate \( x \).
Now, subtract \( d \) from both sides to move the constant to the other side:

\[
a - d = x(b + c)
\]

### Step 3: Solve for \( x \).
Finally, divide both sides by \( (b + c) \) to solve for \( x \):

\[
x = \frac{a - d}{b + c}
\]

So, the solution is:

\[
x = \frac{a - d}{b + c}
\]

Would you like further details or clarifications on this process? 

Here are some related questions you might find helpful:

1. What happens if \( b + c = 0 \) in this equation?
2. How can this equation be used to solve word problems in algebra?
3. What is the geometric interpretation of solving for \( x \) in linear equations?
4. How can you apply factoring to more complex equations?
5. How would this solution change if the equation were quadratic in \( x \)?

**Tip:** Always check the denominator in your solutions. If it becomes zero, the equation might not have a valid solution!

Learn how to solve the linear equation a = bx + cx + d for x with a detailed step-by-step solution. This problem demonstrates factoring and isolating variables in algebraic expressions, suitable for students in Grades 8-10.

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