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Find the missing number so that the equation has no solutions. \newline5x+10=5x + 10 = ____x12x - 12

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Q. Find the missing number so that the equation has no solutions. \newline5x+10=5x + 10 = ____x12x - 12
  1. Identify Equation Solutions: Identify when an equation has no solutions: An equation has no solutions when the coefficients of the variable are the same, but the constants are different.
  2. Set Up Missing Number: Set up the equation with the missing number: 5x+10=5x + 10 = ____x12x - 12. To have no solutions, the coefficients of xx must be equal, and the constants must be different.
  3. Equating Coefficients: Equating the coefficients: Set 55 equal to the missing number's coefficient. So, the missing number is 55.
  4. Check Constants: Check the constants: Since the coefficients are the same, check if the constants are different. 101210 \neq -12, so the constants are indeed different.
  5. Conclude Missing Number: Conclude that the missing number is 55, ensuring no solutions for the equation.