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Find the missing number so that the equation has no solutions.\newline____x−5=−3x−2\_\_\_\_x - 5 = -3x - 2

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline____x−5=−3x−2\_\_\_\_x - 5 = -3x - 2
  1. Identify No Solutions Condition: To determine when the equation has no solutions, we need to look for a situation where the two sides of the equation cannot be made equal for any value of xx. This occurs when the coefficients of xx are the same, but the constants are different.
  2. Analyze Given Equation: Let's analyze the given equation: ____x - 5 = -3x - 2. For the equation 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 −3-3. However, the constants must be different.
  3. Set Coefficient of x to −3-3: So, we set the coefficient of x on the left side to −3-3: −3x−5=−3x−2-3x - 5 = -3x - 2. Now, we have the same coefficients for x on both sides.
  4. Compare Constants: Next, we look at the constants. On the left side, we have −5-5, and on the right side, we have −2-2. Since these constants are different, the equation will have no solutions.
  5. Determine Missing Number: Therefore, the missing number that ensures the equation has no solutions is −3-3.

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