Question

solve the compound inequality. graph the solution set and write it in interval notation.
x ≤ 1 and x ≥ 2
choose the correct graph of the solution set.
solve the compound inequality. 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 \( x \leq 1 \) and \( x \geq 2 \). We need to find the values of \( x \) that satisfy both inequalities simultaneously.

Step2: Determine the solution set

A number cannot be both less than or equal to 1 and greater than or equal to 2 at the same time. There are no such real numbers. So the solution set is the empty set, denoted as \( \varnothing \).

Step3: Match with the graph

Since there are no solutions, the graph should represent an empty set. Looking at the options, the correct graph (though not having a visible one here, but from the logic) and the interval notation for an empty set is \( \varnothing \). Also, for the multiple - choice part about the solution set, option B states that the solution set is \( \varnothing \).

Answer:

For the solution set in interval notation: \( \varnothing \)
For the multiple - choice about the solution set: B. The solution set is \( \varnothing \)