Algebra-2

To solve the inequality |z - 3| < 2, we first break it down into two separate inequalities:

Step 1: Rewrite the Absolute Value Inequality

The expression |z - 3| < 2 means:

-2 < z - 3 < 2

Step 2: Solve the Inequalities

For the left part of the inequality:

−2 < z − 3

Adding 3 to both sides:

1 < z or z > 1

For the right part of the inequality:

z - 3 < 2

Adding 3 to both sides:

z < 5

Step 3: Combine the Results

Combining both inequalities gives us:

1 < z < 5

Identify the Correct Graph

Now, let's match this solution set with the provided graphs:

From the graph, we can see that Graph A is ❌ (does not include values less than 2)

From the graph, we can see that Graph B is ❌ (includes 1, which is not allowed)

From the graph, we can see that Graph C is