A1: A compound inequality is an inequality that combines two or more inequalities using the connectives “and” or “or.” It represents a range of values that satisfy multiple conditions.

Q2: How do I solve a compound inequality?

A2: To solve a compound inequality, solve each inequality separately and then find the common solution set by identifying the values that satisfy all the inequalities simultaneously.

Q3: How do I represent the solution set of a compound inequality graphically?

A3: The solution set of a compound inequality can be represented graphically using a number line. Shade the regions that satisfy each inequality separately and then identify the overlapping region, which represents the common solution set.

Q4: What does an open circle on a number line indicate?

A4: An open circle on a number line indicates that the value is not included in the solution set. It represents an inequality with a strict inequality sign (< or >).

Q5: Can a compound inequality have more than two inequalities?

A5: Yes, a compound inequality can have any number of inequalities combined using the connectives “and” or “or.” The solution set is found by identifying the values that satisfy all the inequalities simultaneously.

In conclusion, the compound inequality −5 < a − 4 < 2 represents a solution set that lies between -1 and 6, excluding both endpoints. This can be graphically represented on a number line as a shaded region between -1 and 6, with open circles at -1 and 6 indicating that these values are not included in the solution set. Compound inequalities are important in mathematics and are used to represent a range of values that satisfy multiple conditions simultaneously. [ad_2]