Question

For the following compound inequality, state whether intersection or union should be used. Then give the solution set in both interval and graph forms.

X<-3 or <<4
Should an intersection or a union be used?
-Union
-Intersection
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
(0) A.The solution set is (..)
(Type your answer in interval notation)
(0) B. The solution set is.

Answer 1

The solution to the compound inequality x < -3 or x < 4 is the union of these sets. In interval notation, this is expressed as (-∞, 4), and graphically, it is illustrated as a shaded line on the number line extending from negative infinity up to, but not including, 4.

Step-by-step explanation:

When considering the compound inequality x < -3 or x < 4, we should use the union because it consists of values that satisfy either of the inequalities. Therefore, the solution is all x-values that are less than 4, since this range includes those that are also less than -3. For the interval notation, the solution set would be written as (-∞, 4). In graph form, this would be represented by a line on the number line extending from negative infinity to 4, with an open circle at 4 indicating that 4 is not included in the set.

To graphically represent this solution, you would sketch a number line and shade the area from left (negative infinity) up to the number 4, again, not including the 4 with an open circle. The shaded region represents all the possible x-values that satisfy the original compound inequality.