Solve for the Missing Factor in ?(5b-3) = 20b-15: Algebraic Equation Practice

Algebraic Factoring with Impossible Solutions

Fill in the missing value:

?(5b3)=20b15 ?(5b-3)=20b-15

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the missing values
00:03 Let's factor 20 into factors 5 and 4
00:07 Let's factor 15 into factors 3 and 5
00:13 Let's mark the common factors
00:16 We can see that the factors don't match the given data
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

Fill in the missing value:

?(5b3)=20b15 ?(5b-3)=20b-15

2

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Start by analyzing the equation ?(5b3)=20b15 ?(5b - 3) = 20b - 15 .

Step 2: Note that the right side of the equation is already in the form of a subtraction: 20b15 20b - 15 .

Step 3: Factor the right side of the equation:

  • Both terms on the right side, 20b 20b and 15-15, can be expressed as multiples of 5. Therefore, factor out 5:

20b15=5(4b3) 20b - 15 = 5(4b - 3)

Step 4: Compare with the left side of the equation:

?(5b3) ?(5b - 3)

Step 5: While both sides aim to express multiplication that mirrors each other structurally, endeavoring to achieve a strict variable ratio equivalence through a diverse scale factor remains void due to differing algebraic expression. Therefore, direct factor parity isn't adhered.

Step 6: Since the expression inside the parentheses has a mismatch that prevents it from matching, algebraically, certain middle scale accessing (like ? ? ) will not yield a uniform factor.

Conclusion: Thus, if followed step-by-step identity accuracy and alignment of circumstances forego a consensus number-winning, thus deeming "No adequate solution" viable.

Therefore, the solution to the problem is No adequate solution.

3

Final Answer

No adequate solution

Key Points to Remember

Essential concepts to master this topic
  • Factoring Rule: Factor out the greatest common divisor from all terms
  • Technique: Factor 20b - 15 = 5(4b - 3) by extracting GCD of 5
  • Check: Compare factored forms: ? × (5b - 3) vs 5 × (4b - 3) ✓

Common Mistakes

Avoid these frequent errors
  • Assuming every equation has a numerical solution
    Don't force a number when expressions don't match = incorrect answer! The expressions (5b - 3) and (4b - 3) are fundamentally different and cannot be made equal by any single multiplier. Always check if the algebraic forms can actually match before solving.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

\( 4x^2 + 6x \)

FAQ

Everything you need to know about this question

Why can't I just divide 20b by 5b to get 4?

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You can't divide term by term like that! You need the entire expressions to match. Here we have ?(5b3) ?(5b - 3) vs 5(4b3) 5(4b - 3) , and (5b - 3) ≠ (4b - 3).

How do I know when an equation has no solution?

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Look for structural mismatches! If after proper factoring the expressions in parentheses are different, like (5b - 3) vs (4b - 3), then no single number can make them equal.

What does 'No adequate solution' mean?

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No adequate solution means there's no number that satisfies the equation. It's a valid mathematical answer - not every equation has a numerical solution!

Could I try different factoring methods?

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You should always try the standard factoring approach first. Factor out the GCD from 20b15 20b - 15 to get 5(4b3) 5(4b - 3) , then compare with the left side.

How can I check if 'no solution' is correct?

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Try assuming any number works and substitute it. For example, if ? = 4, then 4(5b3)=20b12 4(5b - 3) = 20b - 12 , but we need 20b15 20b - 15 . Since -12 ≠ -15, no solution exists!

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