Solve for inequality and represent it on the number line: \( -9<3 x-3 \leq 27 \) pyright reserved

1. Start with the inequality: \[ -9 < 3x - 3 \leq 27 \] 2. Add \(3\) to all parts of the inequality: \[ -9 + 3 < 3x - 3 + 3 \leq 27 + 3 \] Simplifying, we get: \[ -6 < 3x \leq 30 \] 3. Divide every part by \(3\) (since \(3\) is positive, the inequality signs remain unchanged): \[ \frac{-6}{3} < \frac{3x}{3} \leq \frac{30}{3} \] Simplifying, we obtain: \[ -2 < x \leq 10 \] 4. The solution set is: \[ x \in (-2, 10] \] 5. Number Line Representation: - Draw a horizontal line. - Place an open circle at \(-2\) (since \(-2\) is not included). - Place a closed circle at \(10\) (since \(10\) is included). - Shade the region between \(-2\) and \(10\). The number line is represented as follows: \[ \text{---(----○====●----)} \] Here, the open circle at \(-2\) signifies \(x > -2\) and the closed circle at \(10\) signifies \(x \leq 10\).