Question

solve the following compound inequality. graph the solutions.
x < 5 and x > -1

solve the compound inequality. select the correct choice below and, if necessary, fill in
the answer box to complete your choice.
a. the solutions are -1 < x < 5 .
(simplify your answer. type an inequality or a compound inequality.)
b. the solutions are all real numbers.
c. there is no solution.

graph the solutions. choose the correct graph below.
a. number line with open circles at -1 and 5, arrows left from -1 and right from 5
b. empty number line from -7 to 7
c. number line with open circles at -1 and 5, blue between them
d. number line from -7 to 7, fully blue

Explanation:

Step1: Analyze the compound inequality

The compound inequality is \( x < 5 \) and \( x > - 1 \). This means we need to find the values of \( x \) that satisfy both inequalities simultaneously.

Step2: Combine the inequalities

To combine \( x > - 1 \) and \( x < 5 \), we can write it as a single compound inequality \( - 1 < x < 5 \).

Step3: Analyze the graphs

• For option A: The graph shows two separate intervals, which does not represent \( - 1 < x < 5 \).
• For option B: The graph is empty, which is not correct as we have a solution.
• For option C: The graph has an open circle at \( - 1 \) and an open circle at \( 5 \) with the line segment between them, which represents \( - 1 < x < 5 \).
• For option D: The graph shows all real numbers, which is incorrect.

Answer:

The solution to the compound inequality is \( - 1 < x < 5 \), and the correct graph is option C.