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Find the missing number so that the equation has infinitely many solutions.\newline−5x+‾=−5x−16-5x + \underline{\hspace{1cm}} = -5x - 16

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions.\newline−5x+‾=−5x−16-5x + \underline{\hspace{1cm}} = -5x - 16
  1. Identical Form: When does this equation have infinitely many solutions?\newlineInfinitely many solutions occur when the both sides of the equation are identical in form.
  2. Coefficients and Constants: -5x + ____ = -5x - 16\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. Find Missing Constant: 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 −16-16, so that the equation becomes −5x−16=−5x−16-5x - 16 = -5x - 16.
  4. Substitute and Verify: By substituting −16-16 for the blank, we get:\newline−5x−16=−5x−16-5x - 16 = -5x - 16\newlineThis equation is true for all values of xx, which means it has infinitely many solutions.

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