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Find the missing number so that the equation has infinitely many solutions. \newline____x−2=−4x−2\_\_\_\_x - 2 = -4x - 2

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Q. Find the missing number so that the equation has infinitely many solutions. \newline____x−2=−4x−2\_\_\_\_x - 2 = -4x - 2
  1. Analyze Equation: Analyze the equation for conditions of infinitely many solutions. Infinitely many solutions occur when both sides of the equation are identical.
  2. Set Up Missing Number: Set up the equation with the missing number.\newline____×x−2=−4x−2\_\_\_\_\times x - 2 = -4x - 2\newlineTo have infinitely many solutions, the coefficients of xx and the constant terms on both sides must be the same.
  3. Compare Coefficients: Compare the coefficients of xx.\newlineLet the missing coefficient be aa. Then aa should equal −4-4 for the xx terms to match.
  4. Check Constants: Check if the constants match.\newlineThe constants on both sides are −2-2, which are already equal.
  5. Conclude Missing Number: Conclude the value of the missing number. Since the coefficients and constants match when a=−4a = -4, the missing number is −4-4.

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