Final answer:
To solve the inequality -8(x - 2) > -4x + 8, distribute -8, combine like terms, and isolate the variable on one side of the inequality sign. Dividing both sides by -4 and reversing the inequality sign gives x < 2. Therefore, a positive single digit solution to the inequality is 1.
Step-by-step explanation:
To solve the inequality -8(x - 2) > -4x + 8, we need to simplify and isolate the variable on one side of the inequality sign. Let's start by distributing -8 to the terms inside the parentheses: -8x + 16 > -4x + 8. Next, let's combine like terms by subtracting -4x from both sides: -8x + 4x + 16 > -4x + 4x + 8. This simplifies to -4x + 16 > 8. Finally, let's subtract 16 from both sides: -4x + 16 - 16 > 8 - 16. This gives us -4x > -8.
Now, to solve for x, we need to divide both sides by -4, remembering to reverse the inequality sign since we're dividing by a negative number: -4x / -4 < -8 / -4. This simplifies to x < 2. Therefore, a positive single digit solution to the inequality is 1.