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Find the missing number so that the equation has infinitely many solutions.\newline−5x+‾=−5x−11-5x + \underline{\hspace{1cm}} = -5x - 11

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions.\newline−5x+‾=−5x−11-5x + \underline{\hspace{1cm}} = -5x - 11
  1. Identical Coefficients: When does this equation have infinitely many solutions? Infinitely many solutions occur when the both sides of the equation are identical.
  2. Find Missing Constant: −5x+‾=−5x−11-5x + \underline{\quad} = -5x - 11\newlineTo have infinitely many solutions, the coefficients of xx must be the same on both sides, which they already are, and the constants must also be the same.
  3. Make Constants Equal: Since the coefficients of xx are the same, we need to find the missing constant that will make the constants on both sides of the equation equal.\newlineThe missing number must be −11-11, so that the equation becomes −5x−11=−5x−11-5x - 11 = -5x - 11.

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