Simplify the Expression: 3x + 4x + 7 + 2

Q: Why can't I just add all the numbers together?

Because variables and constants are different types of terms! You can't combine $ 3x $ with 7 any more than you can add 3 apples to 7 oranges and get 10 apples.

Q: What makes terms 'like terms'?

Like terms have the exact same variable part. $ 3x $ and $ 4x $ are like terms, but $ 3x $ and $ 3x^2 $ are not!

Q: Can I change the order of terms when simplifying?

Yes! Addition is commutative, so you can rearrange terms to group like terms together. Many students find it helpful to put variable terms first: $ 7x + 9 $.

Q: How do I know my simplified answer is correct?

Your simplified expression should have fewer terms than the original, and you can substitute any value for x to check that both expressions give the same result.

Combining Like Terms with Variable and Constant Terms

$3x+4x+7+2=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's simplify the expression together.

00:09 First, collect the like terms. This step makes it easier to solve.

00:15 Now, calculate by adding those terms. Take your time.

00:22 And there you have it. That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3x+4x+7+2=\text{?}$

Step-by-step solution

Let's simplify the expression $3x + 4x + 7 + 2$ step-by-step:

Step 1: Combine Like Terms Involving $x$
The terms $3x$ and $4x$ are like terms because both involve the variable $x$ . To combine them, add their coefficients:
$3x + 4x = (3 + 4)x = 7x$
Step 2: Combine Constant Terms
The expression includes constant terms $7$ and $2$ . These can be added together to simplify:
$7 + 2 = 9$
Step 3: Write the Simplified Expression
Now, combine the results from Step 1 and Step 2 to form the final simplified expression:
$7x + 9$

Therefore, the simplified expression is $7x + 9$ .

Reviewing the choices provided, the correct choice is:

Choice 2: $7x + 9$

This matches our simplified expression, confirming our solution is correct.

Final Answer

$7x+9$

Key Points to Remember

Essential concepts to master this topic

Like Terms Rule: Only combine terms with identical variables and exponents
Technique: Add coefficients: $3x + 4x = (3 + 4)x = 7x$
Check: Count terms before and after: 4 terms become 2 terms ✓

Common Mistakes

Avoid these frequent errors

Adding all numbers together ignoring variables
Don't add 3 + 4 + 7 + 2 = 16! This treats variables like regular numbers and gives completely wrong answers. Always keep variable terms and constant terms separate when combining.

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 add all the numbers together?

Because variables and constants are different types of terms! You can't combine $3x$ with 7 any more than you can add 3 apples to 7 oranges and get 10 apples.

What makes terms 'like terms'?

Like terms have the exact same variable part. $3x$ and $4x$ are like terms, but $3x$ and $3x^2$ are not!

Can I change the order of terms when simplifying?

Yes! Addition is commutative, so you can rearrange terms to group like terms together. Many students find it helpful to put variable terms first: $7x + 9$ .

What if I have more than two like terms?

Same process! Add all the coefficients together. For example: $2x + 5x + x = (2 + 5 + 1)x = 8x$ . Remember that $x$ means $1x$ !

How do I know my simplified answer is correct?

Your simplified expression should have fewer terms than the original, and you can substitute any value for x to check that both expressions give the same result.

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