Answer:
Let's solve and represent the solutions on a number line for each inequality.
f) |x| > 5
Step 1: Set up two cases based on the absolute value:
Case 1: x > 5
Case 2: x < -5
So, the solutions to the inequality |x| > 5 are x > 5 and x < -5. Now, let's represent these solutions on a number line:
```
-∞---(-5)---(5)---∞
x < -5 x > 5
```
g) |x - 1| ≥ 2
Step 1: Set up two cases based on the absolute value:
Case 1: x - 1 ≥ 2
x - 1 + 1 ≥ 2 + 1
x ≥ 3
Case 2: -(x - 1) ≥ 2
-x + 1 ≥ 2
-x ≥ 2 - 1
-x ≥ 1
Now, remember to reverse the inequality sign when multiplying or dividing by a negative number. So, for Case 2:
x ≤ -1
So, the solutions to the inequality |x - 1| ≥ 2 are x ≥ 3 and x ≤ -1. Now, let's represent these solutions on a number line:
```
-∞---(-1)---(3)---∞
x ≤ -1 x ≥ 3
```