Final answer:
To solve the inequality 4 < -2x + 3 < 9, we isolate the variable x by breaking it down into two separate inequalities. The solution is x > -1/2 and x > -3.
Step-by-step explanation:
To solve the inequality 4 < -2x + 3 < 9, we need to isolate the variable x. Let's break it down into two separate inequalities. Starting with the left side, we have 4 < -2x + 3. Subtracting 3 from both sides, we get 1 < -2x. Dividing both sides by -2, we need to reverse the inequality sign to get x > -1/2.
Moving to the right side of the original inequality, we have -2x + 3 < 9. Subtracting 3 from both sides, we get -2x < 6. Dividing both sides by -2, we need to reverse the inequality sign again to get x > -3. Combining both solutions, we find that x must be greater than -1/2 and -3. So, the solution to the inequality 4 < -2x + 3 < 9 is x > -1/2 and x > -3.