Question

solve the compound inequality. graph the solution set and write it in interval notation.
x<4 and x> - 2
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 \(x < 4\) and \(x>-2\). This means \(x\) lies between \(- 2\) and \(4\).

Step2: Determine the graph

For \(x > - 2\) and \(x < 4\), on a number - line, we have an open circle at \(-2\) (since \(x
eq - 2\)) and an open circle at \(4\) (since \(x
eq4\)) and a line segment connecting them.

Step3: Write in interval notation

The interval notation for \(x\) such that \(-2 < x < 4\) is \((-2,4)\).

Answer:

The correct graph is not shown in the provided options (but it should have an open - circle at \(-2\), an open - circle at \(4\), and a line segment between them).
A. The solution set is \((-2,4)\)