`1/4a-1/16b +3 lt5`
Which of the following is equivalent to the inequality above ?

Options

A. `4a-b lt 8`
B. `4a-b lt 32`
C. `a -4blt 32`
D. `4b-a lt 4`

Explanation

To solve the inequality \( \frac{1}{4}a - \frac{1}{16}b + 3 < 5 \), we will simplify it step by step.

### Step 1: Isolate the fractions
We start with the inequality:
\[ \frac{1}{4}a - \frac{1}{16}b + 3 < 5 \]

### Step 2: Eliminate the fractions
To eliminate the fractions, we can multiply the entire inequality by 16 (the least common multiple of the denominators 4 and 16). Since 16 is positive, the direction of the inequality will not change:
\[ 16 \left( \frac{1}{4}a \right) - 16 \left( \frac{1}{16}b \right) + 16 \cdot 3 < 16 \cdot 5 \]

### Step 3: Simplify the terms
Now, we simplify each term:
\[ 4a - b + 48 < 80 \]

### Step 4: Move constant to the right side
Next, we will subtract 48 from both sides of the inequality:
\[ 4a - b < 80 - 48 \]

### Step 5: Simplify the right side
Calculating the right side gives us:
\[ 4a - b < 32 \]

### Conclusion
Thus, the equivalent inequality is:
\[ 4a - b < 32 \]