The inequality given is:

$|x + 1| \geq 6$

Steps to solve:

1. Break down the absolute value inequality: The expression $|x + 1| \geq 6$ implies two cases:

   • $x + 1 \geq 6$
   • $x + 1 \leq -6$

2. Solve each case:

   • Case 1: $x + 1 \geq 6 \implies x \geq 5$

   • Case 2: $x + 1 \leq -6 \implies x \leq -7$

3. Combine the solutions: The inequality holds true for $x \geq 5$ or $x \leq -7$.

Graphing the solution:

• Draw a number line with key points at $x = -7$ and $x = 5$.
• Shade the region where $x \leq -7$ (i.e., all values to the left of $-7$) and $x \geq 5$ (i.e., all values to the right of $5$).
• Since the inequality is greater than or equal to, include the points $x = -7$ and $x = 5$ with solid circles at these points.

Would you like me to sketch this graph for you, or provide additional details?

Related Questions:

1. What is the difference between strict and non-strict inequalities in graphing?
2. How would the graph change if the inequality was $|x + 1| < 6$?
3. How can absolute value inequalities be solved using a graphical method?
4. Can this inequality be solved using interval notation? If yes, how?
5. What is the general form for solving absolute value inequalities?

Tip: When solving absolute value inequalities, always remember to consider both the positive and negative cases of the expression inside the absolute value.