To find the greatest integer value for m that satisfies the inequality 5m-3 > 8m+21, subtract 8m from both sides, isolate m, and consider that m must be an integer.
To find the greatest integer value for m that satisfies the inequality 5m-3 > 8m+21, we need to solve for m. Let's start by subtracting 8m from both sides of the inequality:
5m - 8m - 3 > 8m - 8m + 21
Simplifying, we get:
-3m - 3 > 21
Next, let's isolate m by adding 3 to both sides of the inequality:
-3m > 24
Finally, divide both sides of the inequality by -3 (remembering to flip the inequality sign since we are dividing by a negative number):
m < -8
Since m must be an integer, the greatest integer value for m is -9.