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Find the missing number so that the equation has no solutions.\newline−4x−1=____x+20-4x - 1 = \_\_\_\_x + 20

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline−4x−1=____x+20-4x - 1 = \_\_\_\_x + 20
  1. Identifying No Solutions: When does this equation have no solutions? An equation has no solutions when the variables on both sides have the same coefficient, but the constants are different, making the equation inconsistent.
  2. Finding Missing Number: −4x−1=-4x - 1 = ____x+20x + 20\newlineWhat is the missing number in the equation?\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.
  3. Comparing Coefficients: The coefficient of xx on the left side is −4-4. To have no solutions, the coefficient of xx on the right side should also be −4-4.
  4. Checking Constants: However, the constants on both sides of the equation must be different. The constant on the left side is −1-1, and on the right side, it is +20+20. Since −1≠+20-1 \neq +20, the equation will have no solutions if the coefficients of xx are the same.

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