$$ {\displaylines3x+4>8-x\\ \placeholder{}} $$

To solve the inequality $3x + 4 > 8 - x$, we can follow these steps:

1. **Add $x$ to both sides** to get rid of the $-x$ on the right side:
   \[
   3x + x + 4 > 8
   \]
   which simplifies to:
   \[
   4x + 4 > 8
   \]

2. **Subtract 4 from both sides** to isolate the term with $x$:
   \[
   4x > 4
   \]

3. **Divide both sides by 4** to solve for $x$:
   \[
   x > 1
   \]

So the solution to the inequality is $x > 1$.

Would you like further details on any of these steps, or do you have any questions?

Here are 5 related questions for practice:
1. Solve the inequality $2x - 5 \geq 3x + 7$.
2. Solve the inequality $4x + 2 \leq 6x - 8$.
3. Solve the inequality $5x + 9 < 2x + 15$.
4. Solve the compound inequality $2x - 3 < 7 \text{ and } x + 1 > 4$.
5. Graph the solution to the inequality $x > 1$ on a number line.

**Tip:** Always check your solution by substituting it back into the original inequality to verify it satisfies the condition.

Learn how to solve the inequality 3x + 4 > 8 - x with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequalities and solving linear equations. Suitable for students in Grades 9-12.

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