Simplify the Expression: 10.1x + 5.2x + 2.4x Step by Step

Combining Like Terms with Decimal Coefficients

Solve the following expression:

10.1x+5.2x+2.4x= ? 10.1x+5.2x+2.4x=\text{ ?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem together.
00:11 First, we will break the numbers into whole parts and remainders.
00:27 Next, group all the whole parts together, and then group the remainders.
01:06 Here, we add all the whole numbers.
01:19 Now, let's add the remainders to the whole numbers.
01:30 And that's how we find the solution to the question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

10.1x+5.2x+2.4x= ? 10.1x+5.2x+2.4x=\text{ ?}

2

Step-by-step solution

The first step is factorising each of the terms in the exercise into a whole number and its remainder:

10x+0.1x+5x+0.2x+2x+0.4x= 10x+0.1x+5x+0.2x+2x+0.4x=

Now we'll combine only the whole numbers:

10x+5x+2x=15x+2x=17x 10x+5x+2x=15x+2x=17x

Next, we will calculate the remainder:

0.1x+0.2x+0.4x=0.3x+0.4x=0.7x 0.1x+0.2x+0.4x=0.3x+0.4x=0.7x

Finally, we are left with the following:

17x+0.7x=17.7x 17x+0.7x=17.7x

3

Final Answer

17.7x x

Key Points to Remember

Essential concepts to master this topic
  • Like Terms: Terms with same variable can be combined by adding coefficients
  • Addition: Add decimal coefficients: 10.1 + 5.2 + 2.4 = 17.7
  • Check: Verify by substituting x = 1: 10.1(1) + 5.2(1) + 2.4(1) = 17.7 ✓

Common Mistakes

Avoid these frequent errors
  • Adding variables instead of coefficients
    Don't add the x's together like 10.1x + 5.2x = 15.3x² = wrong answer! This changes the degree of the expression completely. Always add only the numbers in front of x: 10.1 + 5.2 + 2.4 = 17.7, keeping one x.

Practice Quiz

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FAQ

Everything you need to know about this question

Why can I add these terms together?

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You can combine these terms because they're like terms - they all have the same variable (x) raised to the same power (1). Think of it like having 10.1 apples + 5.2 apples + 2.4 apples = 17.7 apples!

What if the decimals don't line up nicely?

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Line up the decimal points when adding: write 10.1 + 5.2 + 2.4 vertically. You can also convert to fractions if that's easier, but decimal addition works perfectly fine.

Do I need to show all the steps like in the explanation?

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While the explanation breaks it into whole numbers and decimals, you can add directly: 10.1+5.2+2.4=17.7 10.1 + 5.2 + 2.4 = 17.7 . The step-by-step method is just one approach!

What if I had different variables like 3x + 4y?

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You cannot combine them! Different variables (x and y) are not like terms. You can only add coefficients when the variable parts are identical.

How do I check if 17.7x is correct?

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Substitute any value for x into both expressions. Try x = 2: Original gives 10.1(2)+5.2(2)+2.4(2)=35.4 10.1(2) + 5.2(2) + 2.4(2) = 35.4 . Simplified gives 17.7(2)=35.4 17.7(2) = 35.4 . They match!

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