Which Graph Represents the Solution Set of the Compound Inequality? −5

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Which Graph Represents the Solution Set of the Compound Inequality? −5 Adding 4 to both sides, we get: −1 < a. Step 2: Solve the second inequality, a − 4 < 2:
Adding 4 to both sides, we get: a < 6. Now, we have the individual solutions of each inequality. To find the common solution set, we need to find the values of “a” that satisfy both inequalities simultaneously. This can be done by finding the intersection of the two solutions. The first inequality, −1 < a, represents all values of "a" greater than -1. On a number line, this would be a shaded region to the right of -1. The second inequality, a < 6, represents all values of "a" less than 6. This can be represented as a shaded region to the left of 6 on the number line. To find the common solution set, we need to find the overlapping region between the two shaded regions. In this case, the overlapping region is between -1 and 6, excluding both endpoints. Therefore, the graph that represents the solution set of the compound inequality −5 < a − 4 < 2 is a number line with a shaded region between -1 and 6, indicated by open circles at -1 and 6.

FAQs: Q1: What is a compound inequality?
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]