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Let's solve the inequality \( x + 3 \leq 4x - 12 \).

### Step-by-Step Solution:

1. Start by simplifying the inequality:

   \[
   x + 3 \leq 4x - 12
   \]

2. Subtract \( x \) from both sides:

   \[
   3 \leq 3x - 12
   \]

3. Add 12 to both sides:

   \[
   15 \leq 3x
   \]

4. Divide both sides by 3:

   \[
   5 \leq x
   \]

   or equivalently,

   \[
   x \geq 5
   \]

### Interpretation:

The solution to the inequality is \( x \geq 5 \). This means that any value of \( x \) greater than or equal to 5 satisfies the inequality.

### Checking the given options:

- 3: No (since \( x \geq 5 \))
- 4: No
- 7: Yes
- 6: Yes
- 5: Yes

### Correct answers are: 5, 6, and 7.

Would you like more details or explanations?

Here are five related questions for further practice:
1. How would the solution change if the inequality were strict \( x + 3 < 4x - 12 \)?
2. What would happen if the variable \( x \) appeared on both sides with a different coefficient?
3. How do you solve an inequality where there is a negative sign before the variable?
4. How would you solve the inequality if there were fractions involved?
5. Can you graph the solution set on a number line?

**Tip:** Always reverse the inequality symbol when multiplying or dividing both sides by a negative number!

Consider the inequality x + 3 ≤ 4x - 12. Select all the values that are part of the solution set.

Learn how to solve the inequality x + 3 ≤ 4x - 12 through step-by-step methods. This problem involves basic algebraic concepts such as transposing terms and solving linear inequalities. Suitable for students in Grades 7-9.

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