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Find the missing number so that the equation has no solutions.\newline____x−3=5x−20\_\_\_\_x - 3 = 5x - 20

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline____x−3=5x−20\_\_\_\_x - 3 = 5x - 20
  1. Understand Equation: Analyze the equation to understand when it has no solutions. An equation has no solutions when the coefficients of the variable terms are equal, but the constants are different. This creates a contradiction that cannot be resolved.
  2. Set Up with Missing Number: Set up the equation with the missing number.\newline____x - 3 = 5x - 20\newlineTo have no solutions, the coefficient of xx on the left side must be the same as the coefficient of xx on the right side, which is 55.
  3. Determine Constant Terms: Determine the constant terms on both sides of the equation.\newlineThe constant term on the left side is −3-3, and the constant term on the right side is −20-20. Since these constants are already different, we just need to ensure the coefficients of xx are the same.
  4. Find Missing Number: Find the missing number that makes the coefficients of xx equal.\newlineThe missing number must be 55 to match the coefficient on the right side.\newline5x−3=5x−205x - 3 = 5x - 20
  5. Check for Contradiction: Check for a contradiction.\newlineSince the coefficients of xx are the same, but the constants are different (−3≠−20-3 \neq -20), this equation will have no solutions.

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