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Find the missing number so that the equation has infinitely many solutions. \newline−2x+9=____x+9-2x + 9 = \_\_\_\_x + 9

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline−2x+9=____x+9-2x + 9 = \_\_\_\_x + 9
  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 the coefficients of xx on both sides of the equation equal and ensure that the constants are also equal.
  2. Check Constant Equality: The given equation is -2x + 9 = ____x + 9. Since the constants on both sides are already equal (9=99 = 9), we only need to focus on making the coefficients of xx equal.
  3. Ensure Coefficient Equality: To have infinitely many solutions, the coefficient of xx on the left side (−2-2) must be equal to the coefficient of xx on the right side. Therefore, the missing number is −2-2.

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