We will solve the equation step by step:

Given equation:

\[
4 = \frac{3}{7}(3x + 14)
\]

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 7 to get rid of the denominator:

\[
4 \times 7 = 3(3x + 14)
\]

\[
28 = 3(3x + 14)
\]

### Step 2: Distribute the 3 on the right-hand side
Now distribute the 3:

\[
28 = 9x + 42
\]

### Step 3: Move the constant to the other side
Subtract 42 from both sides to isolate the term with \(x\):

\[
28 - 42 = 9x
\]

\[
-14 = 9x
\]

### Step 4: Solve for \(x\)
Divide both sides by 9:

\[
x = \frac{-14}{9}
\]

Thus, the solution is:

\[
x = \frac{-14}{9}
\]

Would you like more details on any part of this solution?

Here are some related questions for practice:
1. Solve: \(5 = \frac{4}{9}(6x + 18)\)
2. Solve: \(7 = \frac{5}{8}(4x - 12)\)
3. Solve: \(6 = \frac{2}{3}(9x + 21)\)
4. Solve: \(2 = \frac{7}{5}(x + 10)\)
5. Solve: \(3 = \frac{9}{4}(2x + 8)\)

**Tip:** When solving equations with fractions, eliminate the fraction by multiplying both sides by the denominator first.

Learn how to solve the linear equation 4 = (3/7)(3x + 14) step-by-step. This problem demonstrates how to eliminate fractions, apply the distributive property, and solve for x. Suitable for students in Grades 8-10.

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