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Find the missing number so that the equation has infinitely many solutions. \newline−5x−5=____x−5-5x - 5 = \_\_\_\_x - 5

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Full solution

Q. Find the missing number so that the equation has infinitely many solutions. \newline−5x−5=____x−5-5x - 5 = \_\_\_\_x - 5
  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 the same.
  2. Make Coefficients Equal: The equation is -5x - 5 = ____x - 5. Since we want the equation to have infinitely many solutions, the missing coefficient of xx on the right side must be the same as the coefficient of xx on the left side, which is −5-5.
  3. Determine Missing Number: Therefore, the missing number is −5-5, making the equation −5x−5=−5x−5-5x - 5 = -5x - 5. This equation is true for all values of xx, which means it has infinitely many solutions.

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