To solve for the number Valerie is thinking of, let's follow the operations she described step-by-step with a variable representing the unknown number.
Let the number be \( x \).
According to Valerie:
- Divide the number by 4: \( \frac{x}{4} \)
- Add 5: \( \frac{x}{4} + 5 \)
- Subtract 6: \( \left(\frac{x}{4} + 5\right) - 6 = 6 \)
Now we can set up the equation:
\[ \frac{x}{4} + 5 - 6 = 6 \]
This simplifies to:
\[ \frac{x}{4} - 1 = 6 \]
Now we will isolate \( \frac{x}{4} \):
\[ \frac{x}{4} = 6 + 1 \] \[ \frac{x}{4} = 7 \]
Next, we solve for \( x \) by multiplying both sides by 4:
\[ x = 7 \times 4 \] \[ x = 28 \]
So, the number Valerie is thinking of is 28.