Simplify the Expression: 3x-2x+3-1 Step by Step

Algebraic Simplification with Like Terms

3x2x+31= 3x-2x+3-1=

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00:00 Solve
00:03 Gathering factors
00:08 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

3x2x+31= 3x-2x+3-1=

2

Step-by-step solution

First, we solve the exercise for x coefficients:

3x2x=x 3x-2x=x

Now, we solve the rest of the exercise:

31=2 3-1=2

Now we obtain:

x+2 x+2

3

Final Answer

x+2 x+2

Key Points to Remember

Essential concepts to master this topic
  • Like Terms: Combine terms with identical variables and powers first
  • Technique: Group variable terms: 3x - 2x = 1x = x
  • Check: Substitute any value: 3(1) - 2(1) + 3 - 1 = 3 ✓

Common Mistakes

Avoid these frequent errors
  • Combining unlike terms incorrectly
    Don't combine x terms with constant terms like 3x + 3 = 6x! Variables and numbers are completely different types of terms. Always group like terms separately: combine x terms together, then combine constant numbers together.

Practice Quiz

Test your knowledge with interactive questions

\( 74+32+6+4+4=\text{?} \)

FAQ

Everything you need to know about this question

What exactly are 'like terms' in algebra?

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Like terms are terms that have exactly the same variable part. For example, 3x and -2x are like terms because they both have 'x'. The numbers 3 and -1 are also like terms because they're both constants (no variables).

Why can't I combine 3x and 3 together?

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Because 3x means 3 times some unknown number, while 3 is just the number 3 by itself. They represent completely different mathematical objects! Think of it like trying to add apples and oranges - they stay separate.

Do I always combine like terms first?

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Yes! Always start by identifying and combining like terms before doing anything else. This makes your expression as simple as possible and prevents mistakes in later steps.

How do I know if I simplified correctly?

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Your final answer should have no more like terms to combine. In this case, x+2 x + 2 is fully simplified because x and 2 are different types of terms that can't be combined further.

What if I get confused about the order of operations?

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For simplifying expressions (not solving equations), focus on combining like terms first. Since we're only adding and subtracting here, you can group terms in any order: (3x - 2x) + (3 - 1) = x + 2.

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