If `5B > 4B + 1, "is" B^2 > 1` ?

Answer

To solve the inequality \( 5B > 4B + 1 \) and determine if \( B^2 > 1 \), we will follow these steps:

### Step 1: Simplify the Inequality
Start with the given inequality:
\[ 5B > 4B + 1 \]

### Step 2: Move Terms Involving \( B \) to One Side
Subtract \( 4B \) from both sides:
\[ 5B - 4B > 1 \]

### Step 3: Combine Like Terms
This simplifies to:
\[ B > 1 \]

### Step 4: Analyze the Result
Now we have established that \( B > 1 \). We need to determine if this implies \( B^2 > 1 \).

### Step 5: Square Both Sides
Since \( B > 1 \), we can square both sides of the inequality:
\[ B^2 > 1^2 \]
This simplifies to:
\[ B^2 > 1 \]

### Conclusion
Thus, we conclude that if \( 5B > 4B + 1 \), then \( B^2 > 1 \) is indeed true.

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