\( 3 x<2 x-3 \) or \( 7 x>4 x-9 \)

Let's solve each inequality step by step and then combine the results. ### 1. Solving \( 3x < 2x - 3 \) **Step 1:** Subtract \( 2x \) from both sides to isolate \( x \). \[ 3x - 2x < -3 \] \[ x < -3 \] **Solution for the first inequality:** \( x < -3 \) --- ### 2. Solving \( 7x > 4x - 9 \) **Step 1:** Subtract \( 4x \) from both sides to isolate \( x \). \[ 7x - 4x > -9 \] \[ 3x > -9 \] **Step 2:** Divide both sides by \( 3 \). \[ x > -3 \] **Solution for the second inequality:** \( x > -3 \) --- ### Combining the Solutions The original problem uses the word "or" between the two inequalities, which means the solution set includes values that satisfy **either** one of the inequalities. - From the first inequality: \( x < -3 \) - From the second inequality: \( x > -3 \) **Combined Solution:** \( x < -3 \) **or** \( x > -3 \) This means **all real numbers except** \( x = -3 \) satisfy at least one of the inequalities. ### Final Answer All real numbers except –3 satisfy one or both inequalities. In other words, x ≠ −3