–3x + 7 > –17

Sure, let's solve the inequality step by step:

1. We start with the inequality –3x + 7 > –17.

2. The goal is to isolate x, so we'll first get rid of the 7 on the left side of the inequality. We do this by subtracting 7 from both sides: –3x > -17 - 7.

3. This simplifies to –3x > -24.

4. Now, we'll get rid of the -3 coefficient on x by dividing both sides of the inequality by -3. Remember, when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So, -3x / -3 < -24 / -3.

5. This simplifies to x < 8.

So, the solution to the inequality –3x + 7 > –17 is x < 8.