Question

solve the compound inequality. graph the solution set and write it in interval notation. x < 3 and x > - 4
choose the correct graph of the solution set.
write the solution set in interval notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is ∅.

Explanation:

Step1: Analyze the compound - inequality

The compound inequality is \(x < 3\) and \(x>-4\). This means \(x\) lies between \(- 4\) and \(3\).

Step2: Determine the graph

The graph of the solution set will have an open - circle at \(-4\) (since \(x > - 4\) and \(-4\) is not included) and an open - circle at \(3\) (since \(x < 3\) and \(3\) is not included), and a line segment between them. Option A shows this correct graph.

Step3: Write in interval notation

The interval notation for \(x>-4\) and \(x < 3\) is \((-4,3)\).

Answer:

A. The solution set is \((-4,3)\)
A. (The graph with an open - circle at \(-4\), an open - circle at \(3\), and a line segment between them)