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

Verified step by step guidance

1. Understand the inequality \( |x| \neq 7 \) means the absolute value of \( x \) is not equal to 7. This excludes the points where \( x = 7 \) and \( x = -7 \).
2. Recall that \( |x| = 7 \) corresponds to the two points \( x = 7 \) and \( x = -7 \) on the number line.
3. Since the inequality is \( |x| \neq 7 \), the solution set includes all real numbers except \( x = 7 \) and \( x = -7 \).
4. On the graph, this will be represented by the entire number line with open circles (or holes) at \( x = 7 \) and \( x = -7 \), indicating these points are not included.
5. Match this description to the graph in Column II that shows all points except \( x = 7 \) and \( x = -7 \) excluded.

Key Concepts

Absolute Value

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For example, |x| = 7 means x is either 7 or -7, since both are 7 units from zero.

Inequalities Involving Absolute Value

An inequality like |x| ≠ 7 means x cannot be exactly 7 or -7, but can be any other real number. Understanding how to interpret and graph such inequalities is essential for matching them to their solution sets.

Graphing Solution Sets on the Number Line

Graphing solution sets involves representing all values that satisfy an equation or inequality on a number line. For |x| ≠ 7, the graph excludes points at 7 and -7, showing all other points shaded or included.