Solve the Expression: Simplifying x + x Using Like Terms

Combining Like Terms with Variable Addition

x+x= x+x=

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00:00 Simply
00:02 Gathering factors
00:04 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

x+x= x+x=

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Step-by-step solution

To solve this algebraic problem, follow these steps:

  • Step 1: Identify the coefficients of the variable x x in the expression x+x x + x . Here, the coefficient for each x x is 1.
  • Step 2: Add the coefficients together. This gives 1+1=2 1 + 1 = 2 .
  • Step 3: Multiply the result by the variable. This results in 2x 2x .

Since the problem is a multiple-choice question, review the available choices to select the correct answer. The expression simplifies to 2x 2x , which corresponds to choice 3: 2x 2x .

Therefore, the solution to the problem is 2x 2x .

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Final Answer

2x 2x

Key Points to Remember

Essential concepts to master this topic
  • Like Terms: Variables with same letter and power combine by adding coefficients
  • Technique: Add coefficients: x + x becomes 1x + 1x = 2x
  • Check: Substitute any value: if x = 3, then 3 + 3 = 6 and 2(3) = 6 ✓

Common Mistakes

Avoid these frequent errors
  • Changing the variable's power when combining
    Don't write x + x = x² or 2x²! This changes multiplication to addition and gives completely wrong results. Always keep the same variable power and only add the coefficients to get 2x.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

\( 3+3+3+3 \)

\( 3\times4 \)

FAQ

Everything you need to know about this question

Why can't I just write x + x = 2?

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Because you're adding two x's, not two numbers! The variable x represents an unknown value, so x + x means that unknown value plus itself, which equals 2 times that unknown value = 2x.

What if there's no number in front of x?

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When you see just x, there's an invisible coefficient of 1! So x + x really means 1x + 1x, and 1 + 1 = 2, giving you 2x.

How is this different from 2 + 2 = 4?

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With numbers like 2 + 2, you get a final answer of 4. With variables like x + x, you can only simplify to 2x because you don't know what x equals!

Can I combine x + y the same way?

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No! You can only combine like terms - variables with the exact same letter and power. Since x and y are different variables, x + y stays as x + y.

What if I have 3x + 2x?

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Same rule applies! Add the coefficients: 3 + 2 = 5, so 3x + 2x = 5x. The variable part stays the same, only the numbers in front get added.

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