Compare Expressions: Is 15x-30 Equal to 45-15-5x+15x?

Algebraic Expressions with Like Terms

Are the expressions the same or not?

15x30 15x-30

45155x+15x 45-15-5x+15x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are the expressions equal?
00:04 Let's simplify the expression, group the terms
00:15 It appears the expressions are not equal
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

Are the expressions the same or not?

15x30 15x-30

45155x+15x 45-15-5x+15x

2

Step-by-step solution

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

  • Step 1: Simplify each given expression.
  • Step 2: Compare the simplified expressions to determine if they are equivalent.

Now, let's work through each step:

Step 1: Simplify the expressions

First expression: 15x30 15x - 30

  • The expression is already simplified as it includes one variable term 15x 15x and one constant term 30-30.

Second expression: 45155x+15x 45 - 15 - 5x + 15x

  • Combine the constants: 4515=30 45 - 15 = 30 .
  • Combine the variable terms: 5x+15x=10x-5x + 15x = 10x .
  • The simplified form of the second expression is: 10x+30 10x + 30 .

Step 2: Compare the simplified expressions

After simplification:

The first expression is 15x30 15x - 30 .

The second expression is 10x+30 10x + 30 .

Clearly, these simplified expressions are not the same.

Therefore, the solution to the problem is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Simplification: Combine like terms and constants separately before comparing
  • Technique: Group variables: 5x+15x=10x-5x + 15x = 10x, then constants: 4515=3045 - 15 = 30
  • Check: Final forms must match exactly: 15x3010x+3015x - 30 ≠ 10x + 30

Common Mistakes

Avoid these frequent errors
  • Comparing expressions without simplifying first
    Don't compare 15x3015x - 30 directly to 45155x+15x45 - 15 - 5x + 15x = wrong conclusion! The second expression looks different but might simplify to the same thing. Always simplify both expressions completely before comparing them.

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 which terms are like terms?

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Like terms have the same variable part! In 5x+15x-5x + 15x, both terms have 'x' so they combine. Constants like 4545 and 15-15 are also like terms.

What if the expressions look completely different?

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That's exactly why we simplify first! 45155x+15x45 - 15 - 5x + 15x looks nothing like 15x3015x - 30, but after combining like terms, we can see they're actually different.

Do I need to put terms in a specific order?

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Not necessarily, but it helps! Writing variables first, then constants (like 10x+3010x + 30) makes it easier to compare with other expressions.

What does it mean for expressions to be 'the same'?

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Two expressions are the same if they simplify to identical forms. Even if they look different at first, if they reduce to the exact same coefficients and constants, they're equivalent.

Can I substitute numbers to check if they're equal?

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You could try substituting values for x, but that's not a complete proof! Two different expressions might give the same result for some values of x but not others. Algebraic simplification is more reliable.

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