Let's solve the equation step by step and fill in the blanks.
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Start with the original equation: \[ 3(x−5)+2x=0 \]
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Distribute \(3\) across \((x-5)\): \[ 3x - 15 + 2x = 0 \]
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Combine like terms: \[ 3x + 2x - 15 = 0 \quad \text{which simplifies to} \quad 5x - 15 = 0 \]
Now we can fill in the blanks:
- The first blank (after \(3x +\)) is -15 (the constant term from distributing).
- The second blank involves the equation \(5x = 15\) (rearranging it to equal zero).
Thus, after solving for \(x\): \[ 5x = 15 \quad \Rightarrow \quad x = \frac{15}{5} \] This gives us \(x = 3\).
The values to fill in the blanks are:
- First blank: -15
- Second blank: 15
- Third blank: 3
So the final responses are:
- 3x + (-15) + 2x = 0
- 5x = 15
- x = 3