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Find the missing number so that the equation has infinitely many solutions.\newline3x+1=‾x+13x + 1 = \underline{\hspace{1cm}}x + 1

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions.\newline3x+1=‾x+13x + 1 = \underline{\hspace{1cm}}x + 1
  1. Identify Equation: 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 the coefficients of xx on both sides of the equation the same.
  2. Ensure Same Constants: The equation is 3x + 1 = ____x + 1. Since the constants on both sides are already the same (both are +1+1), we only need to ensure that the coefficients of xx are the same on both sides for the equation to have infinitely many solutions.
  3. Check Coefficients of xx: The coefficient of xx on the left side of the equation is 33. To have infinitely many solutions, the coefficient of xx on the right side must also be 33.
  4. Determine Missing Number: Therefore, the missing number that makes the equation have infinitely many solutions is 33. The equation becomes 3x+1=3x+13x + 1 = 3x + 1, which is true for all values of xx.

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