https://file.aiquickdraw.com/mathbot/file/1726113712518mon3qkg7.jpg

The inequality in the image is:

\[
4x - 7 \leq -2x + 5
\]

Let's solve it step by step:

1. **Move all terms involving \(x\) to one side**:
   \[
   4x + 2x \leq 5 + 7
   \]
   This simplifies to:
   \[
   6x \leq 12
   \]

2. **Solve for \(x\)**:
   \[
   x \leq \frac{12}{6} = 2
   \]

So, the solution is:

\[
x \leq 2
\]

In interval notation, the solution is:

\[
(-\infty, 2]
\]

Thus, the correct answer is **C**: \( ]-\infty, 2] \).

Would you like further details or have any other questions? Here are five related questions to expand your understanding:

1. How do you graph inequalities on a number line?
2. What is the difference between "less than or equal to" and "strictly less than" in inequalities?
3. Can inequalities change direction under certain operations? If so, when?
4. How do you solve compound inequalities?
5. How do we handle inequalities involving absolute values?

**Tip**: When multiplying or dividing both sides of an inequality by a negative number, remember to reverse the inequality sign!

¿Cuál es el resultado de resolver 4x - 7 ≤ -2x + 5?

This page provides a detailed solution to the inequality 4x - 7 ≤ -2x + 5, covering key concepts in algebra and inequalities. Suitable for students in Grades 8-10.

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