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Find the missing number so that the equation has no solutions.\newline5x−11=____x+75x - 11 = \_\_\_\_x + 7

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline5x−11=____x+75x - 11 = \_\_\_\_x + 7
  1. Understand Criteria for No Solutions: To determine the missing number that would result in no solutions, we need to understand that no solutions occur when the equations have the same coefficients for the variable but different constants.
  2. Identify Given Equation: The equation is 5x - 11 = ____x + 7. For there to be no solutions, the coefficient of xx on both sides must be the same, and the constants must be different.
  3. Check Coefficients: The coefficient of xx on the left side is 55. To have no solutions, the missing coefficient on the right side must also be 55.
  4. Check Constants: Now, let's check the constants. On the left side, we have −11-11, and on the right side, we have +7+7. Since these constants are different, if the coefficients of xx are the same, the equation will have no solutions.
  5. Determine Missing Number: Therefore, the missing number is 55, making the equation 5x−11=5x+75x - 11 = 5x + 7, which has no solutions because it simplifies to 0=180 = 18, which is a contradiction.

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