https://file.aiquickdraw.com/mathbot/file/1729132677532ujppa5qe.jpg

The equation presented in the image is:

\[
\frac{1}{6}d + \frac{2}{3} = \frac{1}{4}(d - 2)
\]

Let's solve it step by step.

### Step 1: Distribute on the right-hand side

First, distribute \(\frac{1}{4}\) across \((d - 2)\):

\[
\frac{1}{6}d + \frac{2}{3} = \frac{1}{4}d - \frac{1}{2}
\]

### Step 2: Eliminate fractions by finding a common denominator

The denominators are 6, 3, 4, and 2. The least common denominator (LCD) for these numbers is 12. Multiply the entire equation by 12 to clear the fractions:

\[
12 \times \left( \frac{1}{6}d + \frac{2}{3} \right) = 12 \times \left( \frac{1}{4}d - \frac{1}{2} \right)
\]

This simplifies to:

\[
2d + 8 = 3d - 6
\]

### Step 3: Rearrange terms to isolate \(d\)

Subtract \(2d\) from both sides:

\[
8 = d - 6
\]

Now, add 6 to both sides:

\[
14 = d
\]

Thus, the solution is:

\[
d = 14
\]

Would you like further details or have any questions? Here are some related questions to think about:

1. How do we find the least common denominator in such equations?
2. What is the general method to solve linear equations involving fractions?
3. How can we check if our solution for \(d\) is correct?
4. How does distributing terms work in algebraic expressions?
5. How do we simplify equations with both fractions and variables?

**Tip:** Always try to eliminate fractions early in an equation to simplify your work!

Solve the equation: (1/6)d + 2/3 = (1/4)(d - 2)

Learn how to solve the linear equation (1/6)d + 2/3 = (1/4)(d - 2) step-by-step, using the distributive property and clearing fractions. Suitable for students in Grades 7-9.

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