1.1 Given the following linear inequality: \( -6<2 x-4 \leq 2 \) 1.1.1 Solve the linear inequality.

To solve the linear inequality: \[ -6 < 2x - 4 \leq 2 \] **Step 1: Isolate the term with \( x \)** Add 4 to all parts of the inequality to eliminate the constant term on the right side of the \( 2x \): \[ -6 + 4 < 2x - 4 + 4 \leq 2 + 4 \] Simplifying each part: \[ -2 < 2x \leq 6 \] **Step 2: Solve for \( x \)** Divide all parts of the inequality by 2 to isolate \( x \): \[ \frac{-2}{2} < \frac{2x}{2} \leq \frac{6}{2} \] Simplifying: \[ -1 < x \leq 3 \] **Solution:** The set of all real numbers \( x \) that satisfy the inequality is: \[ -1 < x \leq 3 \] In interval notation, this is written as: \[ (-1,\ 3] \]