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Find the missing number so that the equation has infinitely many solutions. \newline2x−12=2x+‾2x - 12 = 2x + \underline{\hspace{1cm}}

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline2x−12=2x+‾2x - 12 = 2x + \underline{\hspace{1cm}}
  1. Identify Identical Equations: When an equation has infinitely many solutions, it means that both sides of the equation are identical. To find the missing number that makes the equation have infinitely many solutions, we need to make sure that the constants on both sides of the equation are the same.
  2. Find Missing Constant: The equation is 2x−12=2x+___2x - 12 = 2x + \_\_\_. Since the coefficients of xx are the same on both sides (2x2x), we need to find the constant that will make the right side of the equation equal to the left side.
  3. Ensure Equality of Constants: For the equation to have infinitely many solutions, the constant on the right side must be the same as the constant on the left side. The constant on the left side is −12-12. Therefore, the missing number on the right side must also be −12-12.
  4. Complete the Equation: We can now fill in the missing number to complete the equation: 2x−12=2x−122x - 12 = 2x - 12. This equation has infinitely many solutions because both sides are identical.

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