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Find the missing number so that the equation has no solutions.\newline____x−11=3x−4\_\_\_\_x - 11 = 3x - 4

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline____x−11=3x−4\_\_\_\_x - 11 = 3x - 4
  1. 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 after simplifying the equation.
  2. Set Up Equation: Set up the equation with the missing number. ____x−11=3x−4\_\_\_\_x - 11 = 3x - 4
  3. Determine Coefficient: Determine the coefficient of xx that would make the equation have no solutions.\newlineSince the coefficients of xx must be the same for there to be no solutions, the missing number must be 33.
  4. Check Constants: Check if the constants are different with the found coefficient.\newline3x−11≠3x−43x - 11 \neq 3x - 4\newlineThe constants −11-11 and −4-4 are different, so the equation with the coefficient 33 for xx will have no solutions.
  5. Conclude Missing Number: Conclude the missing number. The missing number is 33, which makes the equation have no solutions.

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