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Find the missing number so that the equation has no solutions.\newline4x−8=____x−14x - 8 = \_\_\_\_x - 1

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Full solution

Q. Find the missing number so that the equation has no solutions.\newline4x−8=____x−14x - 8 = \_\_\_\_x - 1
  1. Identify No Solutions: Understand when an equation has no solutions. An equation has no solutions when the two sides of the equation are parallel lines, which means the coefficients of xx are the same, but the constants are different.
  2. Set Up Equation: Set up the equation 4x - 8 = ____x - 1. To have no solutions, the coefficient of xx on both sides must be the same, but the constants must be different.
  3. Determine Missing Coefficient: Determine the missing coefficient. Since we need the coefficients to be the same for no solutions, the missing number must be 44, so the equation becomes 4x−8=4x−14x - 8 = 4x - 1.
  4. Check for Errors: Check for a math error.\newlineThe equation 4x−8=4x−14x - 8 = 4x - 1 has the same coefficient for xx on both sides, which is correct. However, the constants are different (−8-8 and −1-1), which means the lines are parallel and the equation has no solutions.

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