Question: Solve the equation: \[ -3|2x - 9| = -9 \] NOTE: List your answers as integers or reduced…

Solve the equation:

\[ -3|2x - 9| = -9 \]

NOTE: List your answers as integers or reduced fractions with a comma in between. For example: 5, -2/3

The solutions are:

Solution

The given equation is: \[ -3|2x - 9| = -9 \] First, divide both sides by \(-3\): \[ |2x - 9| = 3 \] Now, consider the two cases for the absolute value. Case 1: \(2x - 9 = 3\) Add 9 to both sides: \[ 2x = 12 \] Divide by 2: \[ x = 6 \] Case 2: \(2x - 9 = -3\) Add 9 to both sides: \[ 2x = 6 \] Divide by 2: \[ x = 3 \] The solutions are: 6, 3.