To solve for \( d \) in the equation:

\[
1 = \frac{d - 6}{3}
\]

we start by isolating \( d \).

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to remove the denominator:

\[
1 \times 3 = \frac{d - 6}{3} \times 3
\]

This simplifies to:

\[
3 = d - 6
\]

### Step 2: Solve for \( d \)
Now, add 6 to both sides to isolate \( d \):

\[
3 + 6 = d
\]

\[
d = 9
\]

### Solution
The value of \( d \) is:

\[
d = 9
\]

Would you like more details or have any questions?

### Related Questions:
1. How would you solve if the equation were \( 2 = \frac{d - 8}{4} \)?
2. What if the fraction had been on the left side, like \( \frac{d - 6}{3} = 1 \)?
3. How would you check if a solution to a similar equation is correct?
4. What happens if \( d - 6 = 0 \) in this equation?
5. Can this equation be solved graphically? If so, how?

#### Tip:
When solving equations with fractions, clearing the fraction by multiplying both sides is often the easiest first step.

Learn how to solve the linear equation 1 = (d - 6) / 3 with a clear, step-by-step solution. This problem covers basic algebraic concepts and techniques, including isolating variables and simplifying equations. Suitable for students in Grades 6-8.

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