\((\mathrm{x} + 5) + (2\mathrm{x} - 3)\)Which of the following is equivalent to the given expression?

1. TRANSLATE the problem information

• Given: The expression \((x + 5) + (2x - 3)\)
• Need to find: An equivalent expression from the answer choices

2. SIMPLIFY by removing parentheses and rearranging

• Since we're adding two expressions, we can remove the parentheses:
  \((x + 5) + (2x - 3) = x + 5 + 2x - 3\)
• Rearrange to group like terms together:
  \(x + 5 + 2x - 3 = x + 2x + 5 - 3\)

3. SIMPLIFY by combining like terms

• Combine the x terms: \(x + 2x = 3x\)
• Combine the constant terms: \(5 - 3 = 2\)
• Final result: \(3x + 2\)

Answer: B. \(3x + 2\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Making sign errors when handling the negative term

Students often get confused about the signs, especially with the \(-3\). They might incorrectly treat \((2x - 3)\) as \((2x + 3)\) or change the sign of the 5 to get expressions like \((x - 5) + (2x - 3)\).

This may lead them to select Choice C (\(3x - 8\)) if they use \((x - 5) + (2x - 3)\), or Choice D (\(3x + 8\)) if they use \((x + 5) + (2x + 3)\).

The Bottom Line:

This problem tests careful attention to positive and negative signs when removing parentheses and combining like terms. The key is to track each term's sign throughout the simplification process.