\[ \begin{array}{l} |2 x-2|=4 \\ x=\square \\ x=\square \end{array} \] (smaller value) (larger value) Additional Materials

To solve the equation \(|2x - 2| = 4\), we need to consider two scenarios due to the absolute value. First, we set up the equation without the absolute value: \(2x - 2 = 4\). Solving this gives \(2x = 6\) or \(x = 3\). Next, we set up the second scenario by flipping the sign: \(2x - 2 = -4\). From this, we find \(2x = -2\) or \(x = -1\). So, the solutions are \(x = -1\) and \(x = 3\). Let’s take a moment to appreciate absolute value equations! They show up everywhere, like when determining distances. Think about this in real-life; if you’re 4 miles away from a certain point, whether you moved 4 miles east or 4 miles west, you're still the same distance from that point—just like how absolute values make distances matter without direction! If you want to dive deeper into the concept of absolute values, consider exploring topics like inequalities and complex numbers. Absolute values relate closely to these areas since they both deal with magnitudes and can open you up to a broader understanding of mathematical principles, including how distances work in different dimensions!