The problem in the image is asking to solve the absolute value inequality:

$\frac{|x + 8|}{7} \geq 1$

Step 1: Remove the fraction

To eliminate the fraction, multiply both sides of the inequality by 7:

$|x + 8| \geq 7$

Step 2: Solve the absolute value inequality

The general rule for solving inequalities of the form $|A| \geq B$ is that:

$A \geq B \quad \text{or} \quad A \leq -B$

In this case, $A = x + 8$ and $B = 7$. So, we split the inequality into two cases:

1. $x + 8 \geq 7$
2. $x + 8 \leq -7$

Step 3: Solve each inequality

1. $x + 8 \geq 7$ $x \geq 7 - 8$ $x \geq -1$

2. $x + 8 \leq -7$ $x \leq -7 - 8$ $x \leq -15$

Final Answer:

The solution to the inequality is: $x \geq -1 \quad \text{or} \quad x \leq -15$

Thus, the answer is:

• $x \geq -1$ and $x \leq -15$.

Would you like any further details or clarification?

Here are some related questions to practice:

1. How do you solve absolute value inequalities involving "<"?
2. Can absolute value inequalities have no solution?
3. What is the difference between strict inequality ($<$ or $>$) and inclusive inequality ($\leq$ or $\geq$)?
4. How do you graph the solution of an absolute value inequality on a number line?
5. Can absolute value inequalities involve quadratic expressions?

Tip: When solving absolute value inequalities, always remember to split the inequality into two cases: one for the positive and one for the negative.