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.

Which number line represents the solution to the compound inequality below? x + 5 < 7 and x > - 1 о O O ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 + + → -5 -4 -3 -2 -1 0 1 2 3 4 5 4H H +0 Đ -5 -4 -3 -2 -1 0 1 2 3 4 5 4+ -5 H -3 -2 # 10 -1 0 1 2 3 4 5

Which number line represents the solution to the compound inequality below? x + 5 < 7 and x > - 1 о O O ++ -5 -4 -3 -2 -1 0 1 2 3 4 5 + + → -5 -4 -3 -2 -1 0 1 2 3 4 5 4H H +0 Đ -5 -4 -3 -2 -1 0 1 2 3 4 5 4+ -5 H -3 -2 # 10 -1 0 1 2 3 4 5

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

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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