Question
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Answer
\( 7(x - 3) = 7x - 21 \)
Solution
It looks like you're working with the expression \( 7(x - 3) \). If you want to expand or simplify this expression, you can use the distributive property. Here's how to do it:
### Distributive Property
The distributive property states that:
\[ a(b + c) = ab + ac \]
In your case, \( a = 7 \), \( b = x \), and \( c = -3 \).
### Applying the Distributive Property
\[ 7(x - 3) = 7 \cdot x + 7 \cdot (-3) \]
### Simplify Each Term
1. \( 7 \cdot x = 7x \)
2. \( 7 \cdot (-3) = -21 \)
### Combine the Terms
\[ 7(x - 3) = 7x - 21 \]
### Final Simplified Form
\[ 7(x - 3) = 7x - 21 \]
**Summary:**
By applying the distributive property, the expression \( 7(x - 3) \) simplifies to \( 7x - 21 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Did you know that distributing a number across a set of parentheses is like sharing candy with friends? You take the number outside (like the candy) and give some to each part inside! So, for \( 7(x-3) \), you'd multiply \( 7 \times x \) to get \( 7x \), and then \( 7 \times -3 \) which equals \(-21\), giving you the final result of \( 7x - 21 \). When dealing with expressions like this, a common mistake is forgetting to distribute the negative sign correctly. Always double-check each term after distributing! In this case, the transition from \( (x-3) \) to \( (7x - 21) \) is where that little negative can sneak in and mislead you if you're not careful. Keep an eye on those signs!
