Question

solve the compound inequality. graph the solution set and write it in interval notation.
x < 4 and x > - 1
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 \( x > - 1 \). This means we are looking for all real numbers \( x \) that are greater than -1 and less than 4.

Step2: Write in interval notation

In interval notation, an open interval \((a,b)\) represents all numbers between \( a \) and \( b \) but not including \( a \) and \( b \). Here, \( a=-1 \) and \( b = 4 \), so the interval notation is \( (-1,4) \).

Step3: Analyze the graphs (for the graph part, we can see that the correct graph should have an open circle at -1 (since \( x > - 1 \), not \( x\geq - 1 \)) and an open circle at 4 (since \( x < 4 \), not \( x\leq4 \)) and the line segment between -1 and 4. But since the question also asks for the solution set in interval notation, we focus on that.

Answer:

The solution set in interval notation is \((-1, 4)\)