Compare Expressions: Is 18x Equal to 2+9x?

Expression Equivalence with Linear Terms

Are the expressions the same or not?

18x 18x

2+9x 2+9x

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Step-by-step video solution

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00:00 Are the expressions equal?
00:02 The expressions are not equal
00:05 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Are the expressions the same or not?

18x 18x

2+9x 2+9x

2

Step-by-step solution

To determine if the expressions 18x 18x and 2+9x 2 + 9x are equivalent, we'll analyze their structures.

  • 18x 18x is a linear expression with a single term involving the variable x x , and its coefficient is 18.
  • 2+9x 2 + 9x consists of two terms: a constant term 2 2 and a linear term 9x 9x with coefficient 9.

For two expressions to be equivalent, each corresponding term must be equal. Here, the expression 18x 18x has no constant term, whereas 2+9x 2 + 9x has a constant term of 2. Furthermore, the linear term coefficients differ: 189 18 \neq 9 .

Therefore, the expressions 18x 18x and 2+9x 2 + 9x are not the same. They structurally differ and cannot be made equivalent just through similar values of x x .

Therefore, the solution to this problem is: No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Equivalence Rule: Expressions are equal only if all corresponding terms match
  • Technique: Compare coefficients: 18x has coefficient 18, while 9x has coefficient 9
  • Check: Test with x=1: 18(1)=18 but 2+9(1)=11, so not equivalent ✓

Common Mistakes

Avoid these frequent errors
  • Focusing only on variable terms and ignoring constants
    Don't compare just 18x and 9x while ignoring the +2 = wrong conclusion! The constant term 2 makes these expressions fundamentally different. Always check that both constant terms AND variable coefficients match exactly.

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

How do I know if two expressions are the same?

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Compare every part: For expressions to be equivalent, they must have identical constant terms and identical coefficients for each variable. If any part differs, they're not the same!

What's the difference between 18x and 2+9x?

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The expression 18x 18x has no constant term (just 18 times x), while 2+9x 2+9x has both a constant term (2) and a different coefficient (9) for x.

Can I test with numbers to see if expressions are equal?

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Yes! Pick any value for x and substitute it into both expressions. If you get different results, the expressions aren't equivalent. But remember: getting the same result for one value doesn't prove they're equal!

Why can't I just ignore the constant term?

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The constant term always affects the result! Even if variable parts were the same, adding 2 to one expression makes it larger by 2 for every possible x value.

What if the coefficients were the same but constants different?

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Still not equivalent! For example, 5x 5x and 3+5x 3+5x have the same coefficient but differ by the constant 3, making them parallel but not equal.

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