Match each equation or inequality in Column I with the graph ofits solution set in Column II. | x | ≠ 7

Verified step by step guidance

1. Step 1: Understand the absolute value notation. The expression \(|x|\) represents the distance of \(x\) from 0 on the number line.
2. Step 2: Recognize that \(|x| \neq 7\) means the distance of \(x\) from 0 is not equal to 7.
3. Step 3: Translate the inequality \(|x| \neq 7\) into two separate conditions: \(x \neq 7\) and \(x \neq -7\).
4. Step 4: Consider the number line. The solution set includes all real numbers except \(x = 7\) and \(x = -7\).
5. Step 5: Match this solution set with the graph that shows a number line with open circles at \(x = 7\) and \(x = -7\), indicating these points are not included in the solution.

Key Concepts

Inequalities

Inequalities are mathematical expressions that show the relationship between two values when they are not equal. In this case, the expression |x| ≠ 7 indicates that the absolute value of x cannot equal 7, meaning x can take any value except for 7 and -7. Understanding how to interpret and graph inequalities is crucial for visualizing their solution sets.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, |7| = 7 and |-7| = 7. In the context of the inequality |x| ≠ 7, it signifies that x can be any value except for the two points where the absolute value equals 7, which are 7 and -7.

Graphing Solution Sets

Graphing solution sets involves representing the solutions of an equation or inequality on a number line or coordinate plane. For the inequality |x| ≠ 7, the graph would show all real numbers except for the points 7 and -7, typically represented with open circles at these points to indicate they are not included in the solution set.