Questions: Consider the following equation: 3x-3-12=0 Using the two equations found in Step 2, enter the solution set using set notation.

Solution Steps

Starting with the equation \(3|x-3|-12=0\), we isolate the absolute value term: \[ 3|x-3| = 12 \] Dividing both sides by 3 gives: \[ |x-3| = 4 \]

Next, we set up two equations based on the definition of absolute value:

1. \(x - 3 = 4\)
2. \(x - 3 = -4\)

Now, we solve each equation for \(x\):

1. From \(x - 3 = 4\): \[ x = 7 \]
2. From \(x - 3 = -4\): \[ x = -1 \]

The solutions we found are \(x = 7\) and \(x = -1\). Therefore, the solution set can be expressed in set notation as: \[ \{-1, 7\} \]

Final Answer