Question

solve the compound inequality. graph the solution set and write it in interval notation.
x < 2 or x < 8
choose the correct graph below.
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 \( x < 2 \) or \( x < 8 \). For "or" inequalities, the solution set is the union of the solution sets of each inequality. The solution to \( x < 2 \) includes all numbers less than 2, and the solution to \( x < 8 \) includes all numbers less than 8. The union of these two sets is all numbers less than 8 (since all numbers less than 2 are already included in numbers less than 8).

Step2: Determine the correct graph

Looking at the options, we need a graph that shows all numbers less than 8. Option C has an open circle at 8 (since \( x < 8 \), not \( x \leq 8 \)) and an arrow pointing to the left (indicating all numbers less than 8).

Step3: Write the solution in interval notation

For \( x < 8 \), in interval notation, this is \( (-\infty, 8) \) because it includes all real numbers from negative infinity up to but not including 8.

Answer:

The correct graph is C. The solution set in interval notation is \((-\infty, 8)\)