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Find the missing number so that the equation has no solutions. \newline____x+14=−4x−8\_\_\_\_x + 14 = -4x - 8

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Full solution

Q. Find the missing number so that the equation has no solutions. \newline____x+14=−4x−8\_\_\_\_x + 14 = -4x - 8
  1. Identify No Solutions: Analyze the equation for no solutions. An equation has no solutions when the coefficients of the variable terms are equal, but the constants are different. This creates parallel lines when graphed, which means they will never intersect.
  2. Set Up Equation: Set up the equation with the missing number. \newline____x+14=−4x−8\_\_\_\_x + 14 = -4x - 8\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 −4-4.
  3. Determine Missing Number: Determine the missing number. The missing number must be −4-4 to have the same coefficient as the right side. Missing number: −4-4
  4. Check Constants: Check if the constants are different.\newlineAfter determining the missing number, we have −4x+14=−4x−8-4x + 14 = -4x - 8. The constants are 1414 and −8-8, which are different. This confirms that the equation has no solutions.

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