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.