Question

solve the following compound inequality. graph the solutions.
$x < 5$ and $x > - 2$
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
(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.
b.
c.
d.

Explanation:

Step1: Analyze the compound inequality

The compound inequality \(x < 5\) and \(x>-2\) means we need to find the values of \(x\) that satisfy both inequalities simultaneously.

Step2: Combine the inequalities

When we combine \(x < 5\) and \(x > - 2\), we get \(-2

Answer:

A. The solutions are \(-2 < x < 5\)
For the graph, we look for a number - line with an open - circle at \(-2\) (since \(x>-2\) and the value \(-2\) is not included) and an open - circle at \(5\) (since \(x < 5\) and the value \(5\) is not included) and the line segment between them. So the correct graph is D.