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Find the missing number so that the equation has infinitely many solutions. \newline3x−11=3x+‾3x - 11 = 3x + \underline{\hspace{1cm}}

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline3x−11=3x+‾3x - 11 = 3x + \underline{\hspace{1cm}}
  1. Identify Equation Pattern: 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 terms on both sides of the equation are the same.
  2. Check Coefficients and Constants: Looking at the equation 3x−11=3x+_3x - 11 = 3x + \_, we can see that the coefficients of xx on both sides are already the same (3x3x). For the equation to have infinitely many solutions, the constants on both sides must also be the same.
  3. Determine Missing Number: Since the left side of the equation has a constant of −11-11, the missing number on the right side must also be −11-11 to make the constants equal. Therefore, the equation becomes 3x−11=3x−113x - 11 = 3x - 11.
  4. Verify Infinitely Many Solutions: Now that we have determined the missing number, we can check the equation to ensure it has infinitely many solutions. Subtracting 3x3x from both sides gives us −11=−11-11 = -11, which is a true statement for all values of xx. This confirms that the equation has infinitely many solutions.

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