Simplify the Expression: 13x + 5 - 4.5x + 7.5x

Q: Why can't I combine 13x with the number 5?

Because 13x means 13 times some unknown number, while 5 is just 5. They're different types! Think of it like apples and oranges - you can't add 13 apples + 5 oranges to get 18 of something.

Q: Do I add or subtract 4.5x in this problem?

You subtract 4.5x because of the minus sign in front of it. So it becomes: $ 13x + 7.5x - 4.5x $. The coefficient calculation is 13 + 7.5 - 4.5 = 16.

Q: What if I get confused with the decimal numbers?

Write them in order and be extra careful with signs! For this problem: 13 + 7.5 - 4.5. Do the addition first: 13 + 7.5 = 20.5, then subtract: 20.5 - 4.5 = 16.

Q: How do I know I combined all the like terms correctly?

Count your terms! The original expression has 3 x-terms and 1 constant. Your final answer should have exactly 1 x-term and 1 constant. If you have more, you missed combining something!

Q: Can I rearrange the terms before combining them?

Yes! You can group like terms together to make it easier: $ (13x + 7.5x - 4.5x) + 5 $. This makes it clearer which terms to combine.

Combining Like Terms with Decimal Coefficients

$13x+5-4.5x+7.5x=$

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Step-by-step video solution

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00:00 Simply

00:05 Gathering factors

00:25 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$13x+5-4.5x+7.5x=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify and combine like terms involving $x$ .
Step 2: Maintain any constant terms separately.

Now, let's work through each step:
Step 1: The expression to simplify is $13x + 5 - 4.5x + 7.5x$ .
Combine the coefficients of $x$ : $13 + 7.5 - 4.5$ .
Carrying out this calculation: $13 + 7.5 - 4.5 = 16$ .

Step 2: The constant term is $5$ , which remains unchanged.

Therefore, the simplified expression is $16x + 5$ .

The correct choice for this expression is choice 1: $16x + 5$ .

Final Answer

$16x+5$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Only variables with same letter and power combine
Technique: Add/subtract coefficients: 13 + 7.5 - 4.5 = 16
Check: Count x-terms (3) and constants (1) before and after ✓

Common Mistakes

Avoid these frequent errors

Trying to combine x-terms with constants
Don't add 13x + 5 = 18x! Variables and numbers are different types that cannot combine. This creates completely wrong expressions. Always keep x-terms separate from constant numbers.

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

Why can't I combine 13x with the number 5?

Because 13x means 13 times some unknown number, while 5 is just 5. They're different types! Think of it like apples and oranges - you can't add 13 apples + 5 oranges to get 18 of something.

Do I add or subtract 4.5x in this problem?

You subtract 4.5x because of the minus sign in front of it. So it becomes: $13x + 7.5x - 4.5x$ . The coefficient calculation is 13 + 7.5 - 4.5 = 16.

What if I get confused with the decimal numbers?

Write them in order and be extra careful with signs! For this problem: 13 + 7.5 - 4.5. Do the addition first: 13 + 7.5 = 20.5, then subtract: 20.5 - 4.5 = 16.

How do I know I combined all the like terms correctly?

Count your terms! The original expression has 3 x-terms and 1 constant. Your final answer should have exactly 1 x-term and 1 constant. If you have more, you missed combining something!

Can I rearrange the terms before combining them?

Yes! You can group like terms together to make it easier: $(13x + 7.5x - 4.5x) + 5$ . This makes it clearer which terms to combine.

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