Let's simplify each expression step by step and then compare them to the given options.

Expression I:

$x + x + x + 1 + 1 + (-1) + 1$

• Combine like terms:
  • $x + x + x = 3x$
  • $1 + 1 - 1 + 1 = 2$

So, Expression I simplifies to: $3x + 2$

Expression II:

$x + x + 1 + (-1) + x + 1 + 1$

• Combine like terms:
  • $x + x + x = 3x$
  • $1 - 1 + 1 + 1 = 2$

So, Expression II also simplifies to: $3x + 2$

Comparing the Simplified Expressions with the Options:

Both Expression I and Expression II simplify to $3x + 2$, so we need to find which option matches this expression.

• Option A: $+1$ — Incorrect.
• Option B: $3x + x + 2$ — Incorrect (this simplifies to $4x + 2$).
• Option C: $2x + x + 2$ — Incorrect (this simplifies to $3x + 2$).
• Option D: $2x + x + 1$ — Incorrect (this simplifies to $3x + 1$).

Therefore, Option C is the correct answer because it simplifies to $3x + 2$, which is equivalent to both expressions.

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Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you identify like terms in an expression?
2. What happens when you add or subtract constants?
3. Can combining like terms change the variables in an expression?
4. Why is simplifying expressions important in solving equations?
5. How does distributing work in more complex expressions?

Tip: Always group like terms (both variables and constants) before simplifying an expression to avoid mistakes.