can someone help me here? it's asking to explain in words where the mistake in the solution of the inequality is.

The mistake occurs in the second to last line. When you divide both sides by a negative number, the inequality sign should flip.

So the answer should be x > -5 instead of x < -5.

Here's why the inequality sign flips

Let's start with the inequality -2x < 10. Add 2x to both sides and we get 0 < 10+2x which is the same as 0 < 2x+10

Then subtract 10 from both sides to end up with -10 < 2x

We can flip both sides of -10 < 2x to end up with 2x > -10. Note the inequality sign flips, as well as the left and right sides.

Afterward, we solve 2x > -10 by dividing both sides by 2 to get x > -5. The inequality sign does not flip when we divide both sides by a positive number.