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Find the missing number so that the equation has no solutions.\newline____x+9=−5x−19\_\_\_\_x + 9 = -5x - 19

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Q. Find the missing number so that the equation has no solutions.\newline____x+9=−5x−19\_\_\_\_x + 9 = -5x - 19
  1. Analyze the equation: Analyze the equation.\newlineFor an equation to have no solutions, the coefficients of the variable terms must be equal, but the constants must be different. This creates parallel lines when graphed, which means they will never intersect.
  2. Set up the equation: Set up the equation with the missing number.\newline____x + 9 = -5x - 19\newlineTo have no solutions, the coefficient of xx on the left side must be the same as the coefficient on the right side, which is −5-5.
  3. Determine the missing number: Determine the missing number. The missing number must be −5-5 to make the coefficients equal. Missing number: −5-5
  4. Check the constants: Check if the constants are different.\newlineAfter determining the missing number, we have −5x+9=−5x−19-5x + 9 = -5x - 19.\newlineThe constants are 99 and −19-19, which are different. This confirms that the equation will have no solutions.

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