Question

Solve the following equation. If there are multiple answers, enter each answer separated by a comma. Enter None None​ if there are no solutions. ∣ − 9 � + 8 ∣ = − 18 ∣−9x+8∣=−18 ​

Answer 1

The equation \( |{-}9x + 8| = {-}18 \) has no solution since the absolute value cannot be negative. There are no real values for \( x \) that satisfy this equation.

Step-by-step explanation:

The original equation provided is \( |{-}9x + 8| = {-}18 \). However, it is immediately clear that this equation has no solution, because the absolute value of a number cannot be negative. By definition, absolute values are either zero or positive, hence \( |{-}9x + 8| \) must be greater than or equal to 0.

No matter what real value \( x \) is assigned, \( |{-}9x + 8| \) cannot equal {-}18. There are no values of \( x \) that would make \( |{-}9x + 8| = {-}18 \) a true statement. Therefore, the answer is None.