Understanding Compound Inequalities

The video tutorial explains compound inequalities, focusing on the use of 'and' and 'or' to determine solutions. It demonstrates graphing compound inequalities on a number line and interpreting the results using interval notation. Two examples are provided: one with a solution and one without, illustrating the concept of intersection and union in inequalities.

What is a compound inequality?

• An inequality with only one condition

• An inequality that combines two inequalities using 'and' or 'or'

• An inequality that has no solution

• An inequality that only uses the word 'or'

When two inequalities are joined by 'and', what is the solution?

• The union of the two solutions

• The solution with the smaller range

• The intersection of the two solutions

• The solution with the larger range

How is the inequality x > -2 represented on a number line?

• With a closed circle on -2 and an arrow to the left

• With an open circle on -2 and an arrow to the right

• With an open circle on -2 and an arrow to the left

• With a closed circle on -2 and an arrow to the right

What does a closed circle on a number line indicate?

• The interval is infinite

• The value is not included in the interval

• The interval is finite

• The value is included in the interval

How is the solution x > -2 and x ≤ 6 expressed in interval notation?

• (-2, 6)

• [-2, 6)

• [-2, 6]

• (-2, 6]

What does the interval notation (-2, 6] mean?

• Excludes both -2 and 6

• Includes both -2 and 6

• Excludes -2 and includes 6

• Includes -2 and excludes 6

In the second example, why is there no solution?

• Because the intervals overlap

• Because both intervals are finite

• Because the intervals do not overlap

• Because both intervals are infinite

What does DNE stand for in the context of inequalities?

• Does Not Enter

• Does Not End

• Does Not Equal

• Does Not Exist

How can the interval x > -2 and x ≤ 6 be expressed differently?

• x ≤ -2 and x > 6

• -2 < x ≤ 6

• x ≥ -2 or x < 6

• x < -2 or x ≥ 6

What is the significance of an open circle on a number line?

• The interval is finite

• The interval is infinite

• The value is not included in the interval

• The value is included in the interval