To solve the compound inequality \(-36 < 3x - 6 < -15\), we will break it down into two parts and solve each part step by step.
Step 1: Solve the left part \[ -36 < 3x - 6 \] Add 6 to both sides: \[ -36 + 6 < 3x \] \[ -30 < 3x \] Now, divide by 3: \[ -10 < x \]
Step 2: Solve the right part \[ 3x - 6 < -15 \] Add 6 to both sides: \[ 3x < -15 + 6 \] \[ 3x < -9 \] Now, divide by 3: \[ x < -3 \]
Step 3: Combine the results From Steps 1 and 2, we have: \[ -10 < x < -3 \]
So the solution to the compound inequality is: \[ -10 < x < -3 \]
Final Answer: D: \(-10 < x < -3\)