https://file.aiquickdraw.com/mathbot/file/1729123232559cwbsrlmn.jpg

The given equation is:

\[
\frac{7w + 4}{6} = \frac{8w - 1}{7} + 1
\]

Let's solve it step by step:

### Step 1: Eliminate the fractions
To get rid of the fractions, multiply both sides of the equation by the least common denominator (LCD) of 6 and 7, which is 42.

\[
42 \times \left(\frac{7w + 4}{6}\right) = 42 \times \left(\frac{8w - 1}{7} + 1\right)
\]

This simplifies to:

\[
7(7w + 4) = 6(8w - 1) + 42
\]

### Step 2: Expand both sides
Now distribute on both sides:

\[
49w + 28 = 48w - 6 + 42
\]

Simplifying the right-hand side:

\[
49w + 28 = 48w + 36
\]

### Step 3: Isolate the variable
Subtract \(48w\) from both sides:

\[
49w - 48w + 28 = 36
\]

This simplifies to:

\[
w + 28 = 36
\]

### Step 4: Solve for \(w\)
Subtract 28 from both sides:

\[
w = 36 - 28
\]

\[
w = 8
\]

### Solution:
The solution is \(w = 8\).

Would you like a detailed explanation of any step? 

Here are some related questions for further practice:
1. How do you solve an equation with variables on both sides?
2. How do you handle equations with multiple fractions?
3. What are some tips for simplifying algebraic expressions?
4. How can you check if your solution is correct?
5. How would the solution change if there were additional terms?

**Tip**: When dealing with fractions in equations, multiplying by the least common denominator (LCD) can help eliminate them and simplify the process.

Solve the equation (7w + 4) / 6 = (8w - 1) / 7 + 1

Learn how to solve an equation with fractions like (7w + 4) / 6 = (8w - 1) / 7 + 1. This step-by-step solution simplifies the equation by eliminating fractions and solving for w. Suitable for students in Grades 8-10.

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