Question

Which inequality’s solution set does the graph represent?

(1 point)
Responses

|x|−4≤5
Start Absolute Value x End Absolute Value minus 4 less-than-or-equal-to 5

12|x+3|≤−4
Start Fraction 1 over 2 End Fraction Start Absolute Value x plus 3 End Absolute Value less-than-or-equal-to negative 4

|x|+5≥9
Start Absolute Value x End Absolute Value plus 5 greater-than-or-equal-to 9

2|x−8|≤14

Answer 1

To determine which inequality's solution set the graph represents, we can analyze each of the given inequalities.

1. **Inequality:** \(|x| - 4 \leq 5\)
**Rearranging:** \(|x| \leq 9\)
**Solution set:** \(-9 \leq x \leq 9\)

2. **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.

3. **Inequality:** \(|x| + 5 \geq 9\)
**Rearranging:** \(|x| \geq 4\)
**Solution set:** \(x \leq -4\) or \(x \geq 4\)

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.