Question

solve the compound inequality. graph the solution set and write it in interval notation.
x < 1 and x > - 4

choose the correct graph of the solution set.
a.
-7 0 7
b.
-7 0 7
c.
-7 0 7
d.
-7 0 7

Explanation:

Step1: Analyze the compound inequality

The compound inequality is \( x < 1 \) and \( x > - 4 \). This means we are looking for all real numbers \( x \) that are greater than - 4 and less than 1. In other words, the solution set is the interval where \( x \) is between - 4 and 1, not including - 4 and 1 themselves.

Step2: Analyze the graphs

• Option A: The graph shows all real numbers, which is not correct as our solution is between - 4 and 1.
• Option B: The graph shows two separate intervals, which is for a compound inequality with "or", but our inequality is "and", so it should be a single interval.
• Option C: The graph has an interval that starts from a point greater than - 7 (close to - 4) and ends less than 1 (close to 0), which matches our solution set \( - 4 < x < 1 \). The open circles indicate that - 4 and 1 are not included.
• Option D: The graph shows no solution, which is incorrect.

Answer:

The correct graph of the solution set is C. The interval notation for the solution set \( - 4 < x < 1 \) is \( (-4,1) \).