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. select the correct choice below and, if necessary, fill in the answer box to complete your choice. the solution set is. simplify your answer. use integers or fractions for any numbers in the expression. type your answer in interval notation. the solution set is

Explanation:

Step1: Analyze the inequalities

We have the compound - inequality \(x < - 3\) and \(x> - 4\). This means we are looking for values of \(x\) that satisfy both inequalities simultaneously.

Step2: Determine the interval

The values of \(x\) that are less than \(-3\) and greater than \(-4\) form the open - interval \((-4,-3)\).

Step3: Graph the solution

On a number line, we mark an open circle at \(-4\) (because \(x\) is greater than \(-4\) but not equal to it) and an open circle at \(-3\) (because \(x\) is less than \(-3\) but not equal to it), and then draw a line segment between them.

Answer:

The solution set in interval notation is \((-4,-3)\) and the correct graph is the one with an open - circle at \(-4\), an open - circle at \(-3\), and a line segment between them.