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Find the missing number so that the equation has no solutions.\newline____x+13=4x12\_\_\_\_x + 13 = -4x - 12

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Q. Find the missing number so that the equation has no solutions.\newline____x+13=4x12\_\_\_\_x + 13 = -4x - 12
  1. Identify Parallel Lines: When does an equation have no solutions?\newlineAn equation has no solutions when the two sides of the equation are parallel lines, which means the coefficients of xx are the same, but the constants are different.
  2. Determine Coefficients: We need to determine the missing number that will make the coefficients of xx the same on both sides of the equation.\newline____x + 13 = -4x - 12\newlineTo have no solutions, the coefficient of xx on the left side must be 4-4.
  3. Check Constants: Now, we need to check if the constants are different with the coefficient we found.\newline4x+13=4x12-4x + 13 = -4x - 12\newlineThe constants are 1313 and 12-12, which are different.
  4. Confirm No Solutions: Since the coefficients are the same and the constants are different, the equation will have no solutions. The missing number is 4-4.