Final answer:
The compound inequality -33 > -3x - 6 > -62 can be transformed into two separate inequalities, leading to the equivalent form -3x - 6 < -33 and -3x - 6 < -62 when solved step-by-step.
Step-by-step explanation:
The compound inequality -33 > -3x - 6 > -62 can be rewritten as two separate inequalities: -3x - 6 > -33 and -3x - 6 < -62. We are separating the compound inequality into two parts, where -3x - 6 is compared to -33 on one side, and to -62 on the other side. Note the inequality symbols have changed direction in the second inequality reflecting the correct relation between -3x - 6 and -62. When we isolate -3x by adding 6 to all parts, we get -27 > -3x > -56. Finally, by dividing the entire inequality by -3 and reversing the inequalities (as we divide by a negative number), we obtain 9 < x < 18.67, fulfilling the original compound inequality.