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Find the missing number so that the equation has no solutions.\newline____x−8=3x+19\_\_\_\_x - 8 = 3x + 19

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline____x−8=3x+19\_\_\_\_x - 8 = 3x + 19
  1. Identify No Solutions: When does this equation have no solutions? An equation has no solutions when the two sides are not equivalent and the variables cancel out, leaving a false statement with the constants.
  2. Analyze Given Equation: Let's analyze the equation ____x - 8 = 3x + 19. For the equation to have no solutions, the coefficients of xx must be the same on both sides, but the constants must be different.
  3. Check Coefficients: The coefficient of xx on the right side is 33. To have no solutions, the coefficient of xx on the left side must also be 33. So, the missing number is 33.
  4. Fill in Missing Number: Now, let's check if the constants are different with the missing number filled in.\newline3x−8=3x+193x - 8 = 3x + 19\newlineIf we subtract 3x3x from both sides, we get:\newline−8≠19-8 \neq 19\newlineThis is a true statement, meaning the constants are different and the equation has no solutions.

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