Simplify by combining like terms: 3u + 9x + 6u + 2x. What is the coefficient of u?
Understand the Problem
The question is asking to simplify the expression by combining like terms, specifically focusing on the coefficients of 'u'. The goal is to find the sum of the coefficients of 'u' in the expression 3u + 9x + 6u + 2x.
Answer
The number that goes in the green box is $9$.
Answer for screen readers
The number that goes in the green box is 9.
Steps to Solve
-
Identify the terms with 'u'
The expression is: $3u + 9x + 6u + 2x$.
The terms with 'u' are $3u$ and $6u$. -
Add the coefficients of 'u'
Combine the coefficients of 'u':
$$ 3 + 6 = 9 $$ -
Construct the simplified expression
Now substitute the sum back into the expression.
The $u$ terms become $9u$, and for the $x$ terms ($9x + 2x$), add them as well:
$$ 9x + 2x = 11x $$
So the complete simplified expression is $9u + 11x$.
The number that goes in the green box is 9.
More Information
This result shows that in the simplified expression, the coefficient of 'u' is 9, indicating that for every unit of 'u', there are 9 units contributed from the original terms.
Tips
- Forgetting to combine all terms: Sometimes, students forget to add all relevant coefficients, especially if there seem to be many variables.
- Mistaking coefficients: Ensure not to confuse coefficients of different variables; focus only on those of 'u' in this context.
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