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The equation given is:

\[
2 = \frac{7}{2} (5x + 6)
\]

Let's solve for \(x\) in the simplest form:

### Step 1: Eliminate the Fraction
Multiply both sides by 2 to eliminate the fraction:

\[
2 \times 2 = \frac{7}{2} (5x + 6) \times 2
\]

\[
4 = 7(5x + 6)
\]

### Step 2: Expand the Right Side
Expand the expression on the right side:

\[
4 = 35x + 42
\]

### Step 3: Isolate \(x\)
Subtract 42 from both sides:

\[
4 - 42 = 35x
\]

\[
-38 = 35x
\]

### Step 4: Solve for \(x\)
Divide both sides by 35:

\[
x = \frac{-38}{35}
\]

So, the solution for \(x\) in simplest form is:

\[
x = -\frac{38}{35}
\]

Would you like further details on any part of the solution? Here are some related questions that might interest you:

1. How do you solve linear equations involving fractions?
2. What are the steps to clear fractions in an equation?
3. How can you check the solution to an equation?
4. What are common mistakes when solving equations like this one?
5. How do you simplify fractions?

**Tip:** Always double-check your work by substituting the solution back into the original equation to verify that both sides are equal!

Solve for x in simplest form: 2 = (7/2)(5x + 6)

Learn how to solve the linear equation involving fractions 2 = (7/2)(5x + 6) with a step-by-step solution. This problem involves expanding and isolating variables, making it ideal for students in Grades 8-10. Clear instructions on how to handle fractions in linear equations are provided.

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