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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.
- Understand Equation Solutions: Understand when an equation has no solutions. An equation has no solutions when the two sides of the equation are parallel lines, which means the coefficients of are the same, but the constants are different.
- Compare Coefficients of : Compare the coefficients of on both sides of the equation.____x - 15 = 4x + 12To have no solutions, the coefficient of on the left side must be the same as the coefficient on the right side, which is .
- Determine Constant Terms: Determine the constant terms on both sides of the equation.Since the coefficients of are the same, we need to ensure that the constants on both sides of the equation are different to have no solutions. The left side has a constant of , and the right side has a constant of . Since is not equal to , the equation will have no solutions if the coefficients of are the same.
- Conclude Missing Number: Conclude the missing number.The missing number is the coefficient of on the left side that will make the equation have no solutions. Since the coefficients must be the same and the constants are already different, the missing number is .
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