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
a. the solution set is (-4,3)
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in
b. the solution set is ∅.

Explanation:

Step1: Analyze the inequalities

We have \(x < 3\) and \(x>-4\). This means \(x\) lies between - 4 and 3.

Step2: Determine interval - notation

Since \(x\) is strictly greater than - 4 and strictly less than 3, in interval - notation, we use open - brackets. The interval is \((-4,3)\).

Step3: Analyze the graph

On a number line, we mark an open - circle at \(x=-4\) (because \(x > - 4\)) and an open - circle at \(x = 3\) (because \(x<3\)) and shade the region between them.

Answer:

A. The solution set is \((-4,3)\)
The correct graph of the solution set is a number line with an open - circle at \(x=-4\), an open - circle at \(x = 3\), and the region between them shaded. Without seeing the full details of the graphs labeled A, B, C, D, we can describe the correct graph as follows: it should have an open - dot at \(-4\) and an open - dot at \(3\) with the line segment between \(-4\) and \(3\) shaded.