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Find the missing number so that the equation has no solutions.\newline____x−10=−5x+7\_\_\_\_x - 10 = -5x + 7

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline____x−10=−5x+7\_\_\_\_x - 10 = -5x + 7
  1. Identify Situation: To determine the missing number that would result in no solutions, we need to create a situation where the equation is never true, regardless of the value of xx. This occurs when the coefficients of xx are the same on both sides of the equation, but the constants are different.
  2. Write Equation: Let's write down the equation with the missing number represented by a blank: _____x−10=−5x+7\_\_\_\_\_x - 10 = -5x + 7. To have no solutions, the coefficient of xx on the left side must be the same as the coefficient on the right side, which is −5-5. Therefore, the missing number is −5-5.
  3. Determine Missing Number: However, for the equation to have no solutions, the constants on both sides must be different. In this case, the constants are already different (−10-10 on the left and +7+7 on the right). So, by having the same coefficients and different constants, the equation will have no solutions.

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