Given - 2x-8>-12 determine the largest integer that satisfies the inequality

-2x - 8 > - 12

-2x - 8 + 2x > - 12 + 2x ... add 2x to both sides

-8 > - 12 + 2x

-8+12 > - 12+2x+12 ... add 12 to both sides

4 > 2x

2x < 4 ... flip both sides so that the x term is on the left side

2x/2 < 4/2 ... divide both sides by 2

x < 2

This describes the set of x values such that x is less than 2.

The largest integer that x can be is x = 1. The value of x cannot be 2 because we don't have an "or equal to" as part of the inequality sign.

Final Answer: 1