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To solve the inequality \( 17.56 + 5x < 30.16 \), let's follow these steps:

### Step 1: Isolate the term with \( x \)
Subtract 17.56 from both sides:

\[
5x < 30.16 - 17.56
\]

### Step 2: Simplify the right side
\[
5x < 12.6
\]

### Step 3: Solve for \( x \)
Divide both sides by 5:

\[
x < \frac{12.6}{5}
\]

\[
x < 2.52
\]

### Answer:
The correct answer is:
**D. \( x < 2.52 \)**

Would you like more details or have any questions?

### Related Questions:
1. How do you solve inequalities involving fractions?
2. What are the rules for flipping inequality signs?
3. How would the inequality change if it were \( 17.56 + 5x \geq 30.16 \)?
4. How do you graph inequalities on a number line?
5. What are some common mistakes when solving inequalities?

### Tip:
Always double-check your calculations when working with inequalities to ensure the correct inequality direction and arithmetic operations!

Learn how to solve the linear inequality 17.56 + 5x < 30.16 with step-by-step guidance. This problem involves fundamental algebraic concepts of inequalities and linear equations, suitable for students in Grades 6-8.

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