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To solve the inequality for the values given in the set \(\{-5, -4, -3, -1, 0, 2\}\), we need to check which of these values satisfy the inequality:

\[
-\frac{1}{2}x + 3 \leq 5
\]

### Step-by-step Solution:
1. **Isolate \(x\)** in the inequality:
   \[
   -\frac{1}{2}x + 3 \leq 5
   \]
   First, subtract 3 from both sides:
   \[
   -\frac{1}{2}x \leq 2
   \]
   Next, multiply both sides by \(-2\) to cancel out the fraction. Remember, when you multiply or divide by a negative number, the inequality sign flips:
   \[
   x \geq -4
   \]

### Conclusion:
The inequality simplifies to \(x \geq -4\). Now we check the values from the set \(\{-5, -4, -3, -1, 0, 2\}\):

- For \(x = -5\): \(-5 \not\geq -4\), so this does **not** satisfy the inequality.
- For \(x = -4\): \(-4 \geq -4\), so this satisfies the inequality.
- For \(x = -3\): \(-3 \geq -4\), so this satisfies the inequality.
- For \(x = -1\): \(-1 \geq -4\), so this satisfies the inequality.
- For \(x = 0\): \(0 \geq -4\), so this satisfies the inequality.
- For \(x = 2\): \(2 \geq -4\), so this satisfies the inequality.

### Final Answer:
The values from the set \(\{-5, -4, -3, -1, 0, 2\}\) that satisfy the inequality are:
\[
\{-4, -3, -1, 0, 2\}
\]

Would you like more details on any specific part of the solution or have any questions?

Here are 5 related questions:
1. How do you solve a linear inequality with fractions?
2. What happens to the inequality sign when you multiply or divide by a negative number?
3. Can you apply the same method for inequalities with greater than or less than symbols?
4. What are some real-life applications of solving inequalities?
5. How would the solution change if the inequality was strict (i.e., \(-\frac{1}{2}x + 3 < 5\))?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Which values from the set {-5, -4, -3, -1, 0, 2} satisfy the inequality -1/2x + 3 ≤ 5?

Learn how to solve the inequality -1/2x + 3 ≤ 5 and determine which values from the set {-5, -4, -3, -1, 0, 2} satisfy the inequality. This problem covers key algebraic concepts and inequality properties. Suitable for students in Grades 7-9.

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