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Find the missing number so that the equation has infinitely many solutions.\newline−4x−19=‾x−19-4x - 19 = \underline{\hspace{1cm}}x - 19

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions.\newline−4x−19=‾x−19-4x - 19 = \underline{\hspace{1cm}}x - 19
  1. Identify Equation Criteria: To determine the missing number that will result in the equation having infinitely many solutions, we need to understand that for an equation to have infinitely many solutions, both sides of the equation must be identical. This means that the coefficients of xx and the constants on both sides must be the same.
  2. Compare Constant Terms: Looking at the equation -4x - 19 = ____x - 19, we can see that the constant term on both sides is already the same, which is −19-19. Therefore, we only need to ensure that the coefficients of xx on both sides are equal.
  3. Ensure Coefficients Equality: Since the coefficient of xx on the left side of the equation is −4-4, the missing number that will make the coefficient of xx on the right side of the equation equal to −4-4 is also −4-4. This will make the equation −4x−19=−4x−19-4x - 19 = -4x - 19.

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