We start with the inequality:

\[
3x + 5 > 8 + 7x
\]

### Step 1: Move the \( x \)-terms to one side
To simplify the inequality, subtract \( 3x \) from both sides:

\[
5 > 8 + 4x
\]

### Step 2: Move the constants to the other side
Now, subtract 8 from both sides:

\[
-3 > 4x
\]

### Step 3: Solve for \( x \)
Finally, divide both sides by 4:

\[
\frac{-3}{4} > x
\]

This simplifies to:

\[
x < \frac{-3}{4}
\]

### Final Solution:
\[
x < -0.75
\]

Let me know if you'd like any further clarification!

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Here are 5 related questions for practice:
1. Solve \( 5x + 7 > 12 + 3x \).
2. Solve \( 6x - 2 \leq 3x + 7 \).
3. Solve \( 4x + 10 > 2x + 20 \).
4. Solve \( 7x + 4 \leq 5x + 8 \).
5. Solve \( 3x - 5 \geq 7x + 1 \).

**Tip**: When solving inequalities, always reverse the inequality sign if you multiply or divide by a negative number.

Learn how to solve the inequality 3x + 5 > 8 + 7x with a detailed, step-by-step solution. This problem covers key algebraic concepts like moving terms, manipulating inequalities, and dividing by negative numbers. Suitable for students in Grades 6-8.

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