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Find the missing number so that the equation has infinitely many solutions. \newline____x−9=−3x−9\_\_\_\_x - 9 = -3x - 9

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline____x−9=−3x−9\_\_\_\_x - 9 = -3x - 9
  1. Identify Equation: To determine the missing number that will result in the equation having infinitely many solutions, we need to make the left side of the equation identical to the right side. The equation is ____x - 9 = -3x - 9.
  2. Ensure Coefficients Match: For the equation to have infinitely many solutions, the coefficients of xx on both sides must be the same, and the constant terms must also be the same.
  3. Check Constant Terms: The constant terms on both sides of the equation are already the same −9 -9 . Therefore, we only need to ensure that the coefficients of x x are the same.
  4. Make Coefficients Equal: The coefficient of xx on the right side of the equation is −3-3. To have infinitely many solutions, the coefficient of xx on the left side must also be −3-3.
  5. Final Equation: Hence, the missing number that makes the coefficient of xx on the left side equal to −3-3 is −3-3 itself. So the equation becomes −3x−9=−3x−9-3x - 9 = -3x - 9.

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