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Find the missing number so that the equation has infinitely many solutions. \newline−3x+5=‾x+5-3x + 5 = \underline{\hspace{1cm}}x + 5

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline−3x+5=‾x+5-3x + 5 = \underline{\hspace{1cm}}x + 5
  1. Identify Identical Expressions: To determine the missing number that will result in the equation having infinitely many solutions, we need to make the expressions on both sides of the equation identical. This means that the coefficients of xx and the constant terms on both sides must be the same.
  2. Ensure Equal Coefficients: The equation is -3x + 5 = ____x + 5. For the equation to have infinitely many solutions, the coefficient of xx on the left side must be the same as the coefficient of xx on the right side. Currently, the coefficient on the left side is −3-3.
  3. Determine Missing Number: Since the coefficients must be the same for the equation to have infinitely many solutions, the missing number that should replace the blank is −3-3. This will make the coefficient of xx on both sides of the equation equal.
  4. Substitute and Confirm: Substituting the missing number, we get −3x+5=−3x+5-3x + 5 = -3x + 5. Now, both sides of the equation are identical, which means the equation has infinitely many solutions.

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