Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point) Responses The equation has no solution. The equation has no solution. The equation has one solution: x=−10. The equation has one solution: x equals negative 10 . The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=0. The equation has one solution: x equals 0 .
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Let's solve the equation step by step:
The original equation is: \[ 4x = 3(x + 5) - 15 \]
First, simplify the right side: \[ 4x = 3x + 15 - 15 \] \[ 4x = 3x \]
Next, subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]
Now we've determined that \(x = 0\) is a solution. Since we derived a single value for \(x\), the equation has one solution.
Thus, the correct response is: The equation has one solution: x = 0.
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