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Find the missing number so that the equation has no solutions.
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Q. Find the missing number so that the equation has no solutions.
- Identify Conditions: Identify the conditions for no solutions.For an equation to have no solutions, the coefficients of the variable terms must be equal, but the constants must be different. This creates parallel lines when graphed, which never intersect.
- Analyze Equation: Analyze the given equation.The given equation is ____x - 16 = -4x + 18. To have no solutions, the coefficient of on the left side must be the same as the coefficient on the right side, which is .
- Set Coefficients Equal: Set the coefficients equal to each other.Since the coefficients must be equal for no solutions, we set the missing coefficient equal to : .
- Determine Constants: Determine the constant terms.For no solutions, the constants must be different. However, in the given equation, the constants are on the left side and on the right side. Since they are already different, we do not need to change anything about the constants.
- Conclude Missing Number: Conclude the missing number.The missing number for the coefficient of on the left side is , as this will make the variable terms on both sides of the equation equal, while the constants remain different, ensuring no solutions.
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