Simplify the Linear Expression: 2a+3-a-2 Step by Step

Combining Like Terms with Rearrangement

2a+3a2= 2a+3-a-2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll use the commutative law and arrange the exercise to make it easier to solve
00:07 Let's group terms
00:12 We'll continue solving according to proper order of operations, from left to right
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

2a+3a2= 2a+3-a-2=

2

Step-by-step solution

We can use the substitutive property and rearrange the exercise in a way that makes it easier for us to solve the exercise:

2aa+32= 2a-a+3-2=

We solve the exercise from left to right:

2aa=a 2a-a=a

32=1 3-2=1

Therefore, we obtain:

a+1 a+1

3

Final Answer

a+1 a+1

Key Points to Remember

Essential concepts to master this topic
  • Like Terms: Combine terms with same variable (2a and -a)
  • Rearrangement: Group like terms together: 2a-a+3-2
  • Check: Substitute a=2: 2(2)+3-2-2 = 5 and 2+1 = 3 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting coefficients incorrectly
    Don't calculate 2a-a as 1 instead of a! This happens when students forget that 'a' means '1a'. Always remember that 2a-a = 2a-1a = (2-1)a = 1a = a.

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why do we rearrange the terms before combining?

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Rearranging helps you see like terms clearly! Grouping 2a-a together and 3-2 together makes it easier to combine without making mistakes.

What does 'a' mean by itself?

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When you see just 'a', it means 1a or one times a. So 2a-a = 2a-1a = 1a = a.

Can I solve this without rearranging?

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Yes! You can work left to right: 2a+3a2 2a+3-a-2 becomes a+32 a+3-2 then a+1 a+1 . But rearranging often prevents errors!

How do I know which terms are 'like terms'?

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Like terms have the exact same variable part. Here, 2a and -a are like terms (both have 'a'), while 3 and -2 are like terms (both are constants).

What if I get a different answer?

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Double-check your arithmetic! The most common errors are: forgetting that a = 1a, or adding/subtracting constants incorrectly. Work step by step and verify your final answer.

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