The inequality in the image is:

$-4|2x - 3| \geq -20$

Step-by-step solution:

1. Divide both sides by -4 (remember that dividing an inequality by a negative number flips the inequality sign):

$|2x - 3| \leq 5$

2. Solve the absolute value inequality:

This inequality $|2x - 3| \leq 5$ can be rewritten as:

$-5 \leq 2x - 3 \leq 5$

3. Solve for $x$ by adding 3 to all parts:

$-5 + 3 \leq 2x \leq 5 + 3$

$-2 \leq 2x \leq 8$

4. Divide by 2:

$-1 \leq x \leq 4$

Final solution:

The solution set is $[-1, 4]$.

The correct answer would be option B, and the solution in interval notation is:

$[-1, 4]$

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you solve absolute value inequalities with a "greater than" symbol?
2. What changes in the solution if the inequality sign had been strict (i.e., $<$ instead of $\leq$)?
3. How do you graph the solution set on a number line?
4. How does dividing or multiplying by a negative number affect inequality signs?
5. Can absolute value inequalities have no solutions? If so, under what conditions?

Tip: When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number!