To determine which inequality's solution set the graph represents, we can analyze each of the given inequalities.
-
Inequality: \(|x| - 4 \leq 5\)
Rearranging: \(|x| \leq 9\)
Solution set: \(-9 \leq x \leq 9\) -
Inequality: \(\frac{1}{2}|x + 3| \leq -4\)
This inequality doesn't have a solution because absolute values are always non-negative and \(-4\) is negative. -
Inequality: \(|x| + 5 \geq 9\)
Rearranging: \(|x| \geq 4\)
Solution set: \(x \leq -4\) or \(x \geq 4\) -
Inequality: \(2|x - 8| \leq 14\)
Rearranging: \(|x - 8| \leq 7\)
Solution set: \(1 \leq x \leq 15\)
If the graph shows a range of \(x\) values indicated by intervals (e.g., from \(-9\) to \(9\) or two separate ranges for the third option), you can match it accordingly.
Please examine the graph you have. If it shows:
- A closed interval from \(-9\) to \(9\), it represents the first inequality: \(|x| - 4 \leq 5\).
- Two separate intervals (one to the left of \(-4\) and one to the right of \(4\)), it represents the third inequality: \(|x| + 5 \geq 9\).
- A closed interval from \(1\) to \(15\), it represents the fourth inequality: \(2|x - 8| \leq 14\).
Given this analysis, you can identify which inequality corresponds to the graph based on its displayed intervals.