We can solve the equation step by step.

Given:
\[
\left( \frac{96 + 30}{20 + 14x} \right) \times 7 = 38.4
\]

### Step 1: Simplify the numerator
\[
96 + 30 = 126
\]
So the equation becomes:
\[
\left( \frac{126}{20 + 14x} \right) \times 7 = 38.4
\]

### Step 2: Divide both sides by 7
\[
\frac{126}{20 + 14x} = \frac{38.4}{7}
\]
\[
\frac{126}{20 + 14x} = 5.4857
\]

### Step 3: Multiply both sides by \((20 + 14x)\)
\[
126 = 5.4857 \times (20 + 14x)
\]

### Step 4: Distribute on the right-hand side
\[
126 = 5.4857 \times 20 + 5.4857 \times 14x
\]
\[
126 = 109.714 + 76.8x
\]

### Step 5: Subtract \(109.714\) from both sides
\[
126 - 109.714 = 76.8x
\]
\[
16.286 = 76.8x
\]

### Step 6: Solve for \(x\)
\[
x = \frac{16.286}{76.8}
\]
\[
x \approx 0.212
\]

So, the solution is:
\[
x \approx 0.212
\]

Would you like more details on any of the steps?

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Here are 5 related questions for further exploration:

1. How would you solve for \(x\) if there was a different coefficient in front of \(x\)?
2. What would happen if the original equation had a different constant on the right-hand side?
3. How do you handle equations involving fractions more efficiently?
4. How would the solution change if the equation involved square roots?
5. Can you set up a similar equation and solve it for a different value of \(x\)?

**Tip:** Always check your solution by plugging it back into the original equation to verify correctness!

Learn how to solve the algebraic equation [(96+30)/(20+14x)]*7=38.4 with a detailed step-by-step breakdown. This problem involves key algebraic concepts such as fraction simplification, solving linear equations, and applying the distributive property. Suitable for students in Grades 8-10.

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