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The problem provided asks to solve the inequality \( 5 - 8x \leq 1 \). Let's solve this step by step.

### Step 1: Isolate the variable term
Subtract 5 from both sides:
\[
-8x \leq 1 - 5
\]
\[
-8x \leq -4
\]

### Step 2: Solve for \( x \)
To solve for \( x \), divide both sides of the inequality by \(-8\). Remember, dividing by a negative number reverses the inequality sign:
\[
x \geq \frac{-4}{-8}
\]
\[
x \geq \frac{1}{2}
\]

So the solution is \( x \geq \frac{1}{2} \).

### Answer:
The correct answer is \( \boxed{E} \).

Would you like any more details or have any other questions?

Here are five related questions:
1. How would the inequality change if the equation was \( 5 - 8x \geq 1 \)?
2. What would happen if you multiplied or divided both sides by a positive number instead of a negative one?
3. Can you solve \( 5 - 8x \leq 2 \) and compare the solution with the original problem?
4. How do you graph the solution of \( x \geq \frac{1}{2} \) on a number line?
5. What is the solution to \( 5x - 8 \leq 1 \) and how does it differ from the given inequality?

**Tip:** Always remember that when you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

The inequality 5 - 8x ≤ 1 is the same as:

Discover how to solve the linear inequality 5 - 8x ≤ 1 using basic algebraic steps. This tutorial covers essential concepts such as reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 8-10.

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