Certainly, let's solve this inequality step by step.
Step 1: The original inequality is 7.8m - 18.2 > 0.8m + 2.8.
Step 2: First we need to simplify the inequality by getting rid of the 0.8m on the right. We can do this by subtracting 0.8m from both sides. This gives: 7.8m - 0.8m - 18.2 > 2.8, which simplifies further to 7.0m - 18.2 > 2.8.
Step 3: Now, we need to isolate the variable m on the left side. We can do this by adding 18.2 to both sides of the equation. This will cancel the -18.2 on the left side. Now, we get: 7.0m > 2.8 + 18.2, which further simplifies to 7.0m > 21.0.
Step 4: The final step to isolate m is to divide both sides of the inequality by 7.0. That gives us: m > 21.0 / 7.0, which simplifies to m > 3.
So the solution to the inequality 7.8m - 18.2 > 0.8m + 2.8 is m > 3.