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Find the missing number so that the equation has no solutions.\newline−5x+4=____x−2-5x + 4 = \_\_\_\_x - 2

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline−5x+4=____x−2-5x + 4 = \_\_\_\_x - 2
  1. Analyze the equation: Analyze the equation -5x + 4 = ____x - 2 to determine when it has no solutions.\newlineAn equation has no solutions when the coefficients of the variable are the same on both sides, but the constants are different.
  2. Compare coefficients of xx: Compare the coefficients of xx on both sides of the equation.\newlineThe coefficient of xx on the left side is −5-5. For the equation to have no solutions, the coefficient of xx on the right side must also be −5-5.
  3. Check constants: Check the constants on both sides of the equation.\newlineThe constant on the left side is +4+4, and the constant on the right side is −2-2. Since these constants are different, if the coefficients of xx are the same, the equation will have no solutions.
  4. Conclude missing number: Conclude the missing number.\newlineThe missing number is the coefficient of xx on the right side that will make the equation have no solutions. Based on our analysis, the missing number is −5-5.

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