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Find the missing number so that the equation has no solutions.\newline____x+2=−2x−1\_\_\_\_x + 2 = -2x - 1

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Q. Find the missing number so that the equation has no solutions.\newline____x+2=−2x−1\_\_\_\_x + 2 = -2x - 1
  1. Identify Conditions: Identify the conditions for no solutions.\newlineFor an equation to have no solutions, the coefficients of the variables must be the same on both sides, but the constants must be different.
  2. Analyze Equation: Analyze the given equation.\newlineThe given equation is x+2=−2x−1x + 2 = -2x - 1.\newlineTo have no solutions, the coefficient of xx on the left side must be the same as the coefficient of xx on the right side, which is \-2.
  3. Determine Missing Number: Determine the missing number.\newlineThe missing number for the coefficient of xx on the left side must be −2-2 to match the right side.
  4. Check Constants: Check the constants on both sides.\newlineThe constants are +2+2 on the left side and −1-1 on the right side. Since they are different, the equation will have no solutions if the coefficients of xx are the same.
  5. Confirm No Solutions: Confirm that the equation has no solutions.\newlineWith the missing number found to be −2-2, the equation becomes −2x+2=−2x−1-2x + 2 = -2x - 1.\newlineSince the coefficients of xx are the same and the constants are different, the equation has no solutions.

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