To determine how many solutions the equation \( 4(x - 5) = 20 - x \) has, we can solve it step by step.
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Distribute the left side: \[ 4(x - 5) = 4x - 20 \] Therefore, we can rewrite the equation as: \[ 4x - 20 = 20 - x \]
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Combine like terms: Add \( x \) to both sides: \[ 4x + x - 20 = 20 \] This simplifies to: \[ 5x - 20 = 20 \]
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Isolate \( x \): Add 20 to both sides: \[ 5x - 20 + 20 = 20 + 20 \] So we have: \[ 5x = 40 \]
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Solve for \( x \): Divide both sides by 5: \[ x = \frac{40}{5} = 8 \]
The equation \( 4(x - 5) = 20 - x \) has one solution, specifically \( x = 8 \).
The answer is:
A. One solution
1 answer