Final answer:
To solve the inequality -3|2x+5|≤-33, divide by -3, remember to reverse the inequality, getting |2x+5|≥11. There are two solutions, x≥3 and x≤-8, representing the range of numbers that satisfy the original inequality.
Step-by-step explanation:
To solve the inequality -3|2x+5|≤-33, we can start by dividing both sides of the inequality by -3. However, remember that dividing by a negative number reverses the inequality sign.
So, the inequality becomes |2x+5|≥ 11.
Next, we split the absolute value equation into two possible cases, considering that the expression inside the absolute value can be either positive or negative. We have:
- Case 1: If 2x+5 is positive, we drop the absolute value and have 2x+5≥11, which simplifies to x≥ 3.
- Case 2: If 2x+5 is negative, we consider the negative of the expression inside, meaning -(2x+5)≥11, which simplifies to x≤ -8.
Therefore, the two solutions for the inequality are any x≥ 3 and any x≤ -8.