a) To solve the equation x * 5400 = 5401 * 30 + 5401, we can start by simplifying the right side of the equation:

5401 * 30 + 5401 = 162030 + 5401 = 167431

Now we can rewrite the equation as:

x * 5400 = 167431

To solve for x, we divide both sides of the equation by 5400:

x = 167431 / 5400

Using a calculator, we find that x is approximately 30.98.

b) To solve the inequality 1000 < 5 * x + 100 < 1010, we can start by subtracting 100 from all parts of the inequality:

1000 - 100 < 5 * x + 100 - 100 < 1010 - 100

900 < 5 * x < 910

Next, we divide all parts of the inequality by 5:

900 / 5 < 5 * x / 5 < 910 / 5

180 < x < 182

Therefore, the solution to the inequality is x is greater than 180 and less than 182.