Absolute Value Inequality 6A44E7

1. **State the problem:** We want to find which absolute value inequality corresponds to the intervals $x \leq -4$ or $x \geq 10$. 2. **Recall the absolute value inequality form:** For $|x - a| \geq b$, the solution is $x \leq a - b$ or $x \geq a + b$. 3. **Check each option:** - A) $|x - 3| \leq 7$ means $-7 \leq x - 3 \leq 7$ which simplifies to $-4 \leq x \leq 10$. This is the interval between $-4$ and $10$, not outside. - B) $|x + 3| \geq 7$ means $x + 3 \leq -7$ or $x + 3 \geq 7$, which simplifies to $x \leq -10$ or $x \geq 4$. This does not match the intervals. - C) $|x - 3| \geq 7$ means $x - 3 \leq -7$ or $x - 3 \geq 7$, which simplifies to $x \leq -4$ or $x \geq 10$. This matches exactly. - D) $|x - 7| \geq 3$ means $x - 7 \leq -3$ or $x - 7 \geq 3$, which simplifies to $x \leq 4$ or $x \geq 10$. This is close but the left interval is $x \leq 4$, not $x \leq -4$. 4. **Conclusion:** The correct inequality is option C) $|x - 3| \geq 7$. **Final answer:** $|x - 3| \geq 7$