Let's solve the equation step by step in order to fill in the blanks correctly.
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Start with the original equation: \( 3(x - 5) + 2x = 0 \)
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Distribute \( 3 \) into \( (x - 5) \): \( 3x - 15 + 2x = 0 \)
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Combine like terms: \( 3x + 2x - 15 = 0 \) So, we combine \( 3x + 2x \) to get: \( 5x - 15 = 0 \)
Now, we can fill in the blanks based on what we found:
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The complete equation is: \( 3x - 15 + 2x = 0 \) Fill in the blank: \(-15\)
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After combining like terms: \( 5x = 15 \) Fill in the blank: \(15\)
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To solve for \( x \): Divide both sides by \( 5 \): \( x = 3 \) Fill in the blank: \(3\)
Putting it all together:
- \( 3(x - 5) + 2x = 0 \) becomes \( 3x - 15 + 2x = 0 \)
- Combine the terms to get \( 5x - 15 = 0 \)
- Solving gives \( x = 3 \)
Final responses for each blank:
- -15
- 15
- 3