First, let's solve the given inequality to verify the solution:

The inequality is $|4x + 6| \leq 10$.

Step 1: Break the absolute value inequality into two cases

1. $4x + 6 \leq 10$
2. $-(4x + 6) \leq 10$

Step 2: Solve each inequality

1. $4x + 6 \leq 10$: $4x \leq 4 \implies x \leq 1$

2. $-(4x + 6) \leq 10$: $-4x - 6 \leq 10 \implies -4x \leq 16 \implies x \geq -4$

Step 3: Combine results

$-4 \leq x \leq 1$

This matches option B as the correct choice.

Additional Problems

1. Solve the inequality: $|3x - 5| > 7$

2. Solve for $x$: $|2x + 3| + 4 = 10$

Let me know if you’d like detailed solutions to these! Here's a quick tip: always isolate the absolute value expression before solving.