
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![The problem asks, "Which number line represents the solution to the compound inequality below?"
The compound inequality given is:
\[ x + 5 \leq 7 \quad \text{and} \quad x > -1 \]
Below the problem, there are four number lines presented as options. Each number line is labeled with numbers from -5 to 5. Each number line also includes circles and shaded regions to represent possible solutions to the inequality.
1. **First Number Line:**
- The number line has an open circle at \( x = -1 \) and a closed circle at \( x = 2 \).
- The shaded region extends to the left from -1 and to the right from 2, excluding these values.
2. **Second Number Line:**
- The number line has a closed circle at \( x = 2 \).
- The shaded region extends from \( x = -5 \) to \( x = 2 \) and is inclusive of these values, with arrows indicating the shading continues beyond -5 to the left.
3. **Third Number Line:**
- The number line has an open circle at \( x = -1 \) and a closed circle at \( x = 2 \).
- The shaded region extends between -1 and 2, exclusively including values greater than -1 and up to and including 2.
4. **Fourth Number Line:**
- The number line has an open circle at \( x = 2 \).
- The shaded region extends from \( x = -1 \) to \( x = 2 \), exclusively including values greater than -1 up to 2, but not including 2.
To solve the compound inequality:
- \( x + 5 \leq 7 \) simplifies to \( x \leq 2 \).
- \( x > -1 \).
Thus, the solution is for \( x \) values greater than -1 and up to and including 2, which corresponds to the third number line.](https://content.bartleby.com/qna-images/question/ebb4bd3b-5f03-40b7-9497-89f3aabd3ed1/f02503c1-f827-49f6-b21f-1cba86566298/wly7dyk_thumbnail.jpeg)
Transcribed Image Text:The problem asks, "Which number line represents the solution to the compound inequality below?"
The compound inequality given is:
\[ x + 5 \leq 7 \quad \text{and} \quad x > -1 \]
Below the problem, there are four number lines presented as options. Each number line is labeled with numbers from -5 to 5. Each number line also includes circles and shaded regions to represent possible solutions to the inequality.
1. **First Number Line:**
- The number line has an open circle at \( x = -1 \) and a closed circle at \( x = 2 \).
- The shaded region extends to the left from -1 and to the right from 2, excluding these values.
2. **Second Number Line:**
- The number line has a closed circle at \( x = 2 \).
- The shaded region extends from \( x = -5 \) to \( x = 2 \) and is inclusive of these values, with arrows indicating the shading continues beyond -5 to the left.
3. **Third Number Line:**
- The number line has an open circle at \( x = -1 \) and a closed circle at \( x = 2 \).
- The shaded region extends between -1 and 2, exclusively including values greater than -1 and up to and including 2.
4. **Fourth Number Line:**
- The number line has an open circle at \( x = 2 \).
- The shaded region extends from \( x = -1 \) to \( x = 2 \), exclusively including values greater than -1 up to 2, but not including 2.
To solve the compound inequality:
- \( x + 5 \leq 7 \) simplifies to \( x \leq 2 \).
- \( x > -1 \).
Thus, the solution is for \( x \) values greater than -1 and up to and including 2, which corresponds to the third number line.
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