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Find the missing number so that the equation has no solutions.\newline____x−16=5x+19\_\_\_\_x - 16 = 5x + 19

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Q. Find the missing number so that the equation has no solutions.\newline____x−16=5x+19\_\_\_\_x - 16 = 5x + 19
  1. Equation with Parallel Lines: An equation has no solutions when the two sides of the equation are parallel lines, which means the coefficients of the variable xx must be the same on both sides, but the constants must be different.
  2. Given Equation Analysis: Given the equation ____x - 16 = 5x + 19, for it to have no solutions, the coefficient of xx on the left side must be the same as on the right side.
  3. Coefficient Matching: Therefore, the missing number for the coefficient of xx on the left side must be 55.
  4. Constant Check: Now, let's check if the constants are different with the missing number filled in. The left side has a constant of −16-16, and the right side has a constant of +19+19.
  5. No Solutions Conclusion: Since −16-16 is not equal to +19+19, the equation 5x−16=5x+195x - 16 = 5x + 19 has no solutions because the lines represented by these equations are parallel and will never intersect.

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