https://file.aiquickdraw.com/mathbot/file/1727380549405f24opbx1.jpg

Solve this using equivalent adjustments​​​

Let's solve the equation using equivalent adjustments. The equation given in the image is:

\[
\frac{3x + 2}{4} = \frac{2}{7}
\]

### Step-by-Step Solution:

1. **Eliminate the denominators** by multiplying both sides of the equation by 28, the least common multiple (LCM) of 4 and 7:

   \[
   28 \cdot \frac{3x + 2}{4} = 28 \cdot \frac{2}{7}
   \]

   This simplifies to:

   \[
   7(3x + 2) = 4 \cdot 2
   \]

   \[
   7(3x + 2) = 8
   \]

2. **Expand the left side** by distributing the 7:

   \[
   21x + 14 = 8
   \]

3. **Isolate the variable term** by subtracting 14 from both sides:

   \[
   21x = 8 - 14
   \]

   \[
   21x = -6
   \]

4. **Solve for \(x\)** by dividing both sides by 21:

   \[
   x = \frac{-6}{21} = \frac{-2}{7}
   \]

Thus, the solution is:

\[
x = \frac{-2}{7}
\]

Would you like more details on any step or have further questions?

Here are 5 related questions you might find interesting:
1. How do you find the least common multiple of two numbers?
2. How would you solve a similar equation but with different fractions?
3. What other methods can be used to solve fractional equations?
4. How do you handle cases where the fractions involve negative numbers?
5. Can the equation be solved by cross-multiplication? How?

**Tip:** Always simplify the fractions early in equations to make calculations easier.

Learn how to solve linear equations involving fractions by eliminating denominators and using the distributive property. This guide provides a step-by-step approach to solving the equation (3x + 2)/4 = 2/7, suitable for students in Grades 6-8.

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