Simplify the Expression: 2x-x+2-1 Using Like Terms

Q: What are like terms exactly?

Like terms have the exact same variable parts. In $ 2x - x + 2 - 1 $, the terms 2x and -x are like terms because both have just 'x'. The numbers 2 and -1 are also like terms (constants).

Q: Why can't I just add all the numbers: 2 + (-1) + 2 + (-1)?

Because 2x and x are not the same as plain numbers! The 'x' makes them variable terms, while 2 and -1 are constant terms. You must keep them separate and only combine within each group.

Q: How do I combine 2x - x?

Think of it as 2x - 1x = (2-1)x = 1x = x. Just like 2 apples minus 1 apple equals 1 apple, but we write it simply as 'x' instead of '1x'.

Q: What if I had 3x terms instead of 2?

Same process! For example: $ 5x - 2x + x = (5-2+1)x = 4x $. Add or subtract the coefficients (numbers in front) and keep the variable part the same.

Q: Can I rearrange the terms before combining?

Absolutely! You can write $ 2x - x + 2 - 1 $ as $ 2x - x + 2 - 1 $ or group them: $ (2x - x) + (2 - 1) $. The order doesn't matter when adding and subtracting.

Combining Like Terms with Mixed Variables

$2x-x+2-1=$

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Step-by-step video solution

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00:00 Solve

00:03 Gathering factors

00:06 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$2x-x+2-1=$

Step-by-step solution

First, we combine the x coefficients:

$2x-x=x$

Now we get the exercise:

$x+2-1=x+1$

Final Answer

$x+1$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Combine terms with same variables and same powers
Technique: Group x terms: 2x - x = (2-1)x = x
Check: Substitute x=0: 2(0)-0+2-1 = 1, and 0+1 = 1 ✓

Common Mistakes

Avoid these frequent errors

Adding all numbers together without grouping like terms
Don't add 2x - x + 2 - 1 = 4x - 2! This ignores that x-terms and constant terms are different types. Variables and numbers can't be combined directly. Always group like terms first: combine x-terms (2x - x = x), then combine constants (2 - 1 = 1).

Practice Quiz

Test your knowledge with interactive questions

$74+32+6+4+4=\text{?}$

FAQ

Everything you need to know about this question

What are like terms exactly?

Like terms have the exact same variable parts. In $2x - x + 2 - 1$ , the terms 2x and -x are like terms because both have just 'x'. The numbers 2 and -1 are also like terms (constants).

Why can't I just add all the numbers: 2 + (-1) + 2 + (-1)?

Because 2x and x are not the same as plain numbers! The 'x' makes them variable terms, while 2 and -1 are constant terms. You must keep them separate and only combine within each group.

How do I combine 2x - x?

Think of it as 2x - 1x = (2-1)x = 1x = x. Just like 2 apples minus 1 apple equals 1 apple, but we write it simply as 'x' instead of '1x'.

What if I had 3x terms instead of 2?

Same process! For example: $5x - 2x + x = (5-2+1)x = 4x$ . Add or subtract the coefficients (numbers in front) and keep the variable part the same.

Can I rearrange the terms before combining?

Absolutely! You can write $2x - x + 2 - 1$ as $2x - x + 2 - 1$ or group them: $(2x - x) + (2 - 1)$ . The order doesn't matter when adding and subtracting.

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