Let's solve the equation step by step, filling in the missing terms and selecting the correct descriptions.
Starting with the given equation:
\[ -3(-4q + 9) = 16q - 11 \]
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Apply the distributive property: \[ -3(-4q) + (-3)(9) = 16q - 11 \] This simplifies to: \[ 12q - 27 = 16q - 11 \]
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Now we have: \[ 12q - 27 = 16q - 11 \]
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We want to isolate q. Start by moving all terms involving q to one side. Subtract 12q from both sides: \[ -27 = 16q - 12q - 11 \] Simplifying gives: \[ -27 = 4q - 11 \]
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Next, add 11 to both sides: \[ -27 + 11 = 4q \] Simplifying gives: \[ -16 = 4q \]
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Now, divide both sides by 4 to solve for q: \[ q = \frac{-16}{4} \] Simplifying gives: \[ q = -4 \]
So, the completed process looks like this:
\[ -3(-4q + 9) = 16q - 11 \quad \text{(Original equation)} \] \[ 12q - 27 = 16q - 11 \quad \text{(After applying the distributive property)} \] \[ -27 = 4q - 11 \quad \text{(After subtracting 12q from both sides)} \] \[ -16 = 4q \quad \text{(After adding 11 to both sides)} \] \[ q = -4 \quad \text{(After dividing both sides by 4)} \]
Fill in the missing terms and descriptions:
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Original Equation \[ -3(-4q + 9) = 16q - 11 \]
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Fill in the blank after applying the distributive property \[ 12q - 27 = 16q - 11 \] Description: Apply the distributive property
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Fill in the blank after moving q terms \[ -27 = 4q - 11 \] Description: Subtract 12q from both sides
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Fill in the blank after adding 11 \[ -16 = 4q \] Description: Add 11 to both sides
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Final result \[ q = -4 \] Description: Divide both sides by 4
Missing Descriptions:
- Apply the distributive property
- Subtract 12q from both sides
- Add 11 to both sides
- Divide both sides by 4
Thus, the solution is \( q = -4 \).
1 answer