We are given the equation:

\[
12 = \frac{2}{7}(5x + 2)
\]

### Steps to solve for \( x \):

1. Multiply both sides of the equation by 7 to eliminate the fraction:

\[
7 \times 12 = 7 \times \frac{2}{7}(5x + 2)
\]

\[
84 = 2(5x + 2)
\]

2. Distribute the 2 on the right-hand side:

\[
84 = 10x + 4
\]

3. Subtract 4 from both sides:

\[
84 - 4 = 10x
\]

\[
80 = 10x
\]

4. Divide both sides by 10:

\[
x = \frac{80}{10}
\]

\[
x = 8
\]

Thus, the solution is \( x = 8 \).

Would you like further details on any of the steps? Here are 5 related questions to expand on this:

1. How do you handle equations with different fractions on both sides?
2. What is the distributive property, and why is it important in solving equations?
3. How can I solve equations with variables on both sides?
4. Can I solve this equation using graphing methods?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always check your answer by substituting it back into the original equation to ensure it's correct.

Learn how to solve the linear equation 12 = (2/7)(5x + 2) using algebraic techniques such as multiplying both sides by the reciprocal and applying the distributive property. Suitable for students in Grades 6-8, this step-by-step guide simplifies the process.

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