Questions: Solve the compound inequality. Graph the solution set and write it in interval notation. x<1 and x>-1 Write the solution set in interval notation. Select the correct choice below and, if necessary, fill A. The solution set is B. The solution set is ∅.

Solve the compound inequality. Graph the solution set and write it in interval notation.
x<1 and x>-1

Write the solution set in interval notation. Select the correct choice below and, if necessary, fill
A. The solution set is
B. The solution set is ∅.

Transcript text: Solve the compound inequality. Graph the solution set and write it in interval notation. \[ x<1 \text { and } x>-1 \] Write the solution set in interval notation. Select the correct choice below and, if necessary, fill A. The solution set is $\square$ B. The solution set is $\varnothing$.

Solution

Solution Steps

Step 1: Analyze the inequalities

We are given two inequalities: $x < 1$ and $x > -1$. We are looking for values of $x$ that satisfy both inequalities simultaneously.

Step 2: Visualize on the number line

The inequality $x < 1$ represents all numbers less than 1. The inequality $x > -1$ represents all numbers greater than -1. The solution set will be the overlapping region where both inequalities are true. This is the region between -1 and 1, excluding -1 and 1.

Step 3: Write the solution in interval notation

The solution set in interval notation is $(-1, 1)$. This means all numbers between -1 and 1, excluding -1 and 1. The graph would be an open circle at -1 and an open circle at 1, with the line shaded between them, corresponding to graph C.