#### Answer

The solution is $(-101,-99)$

#### Work Step by Step

$|0.01x+1|\lt0.01$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-0.01\lt0.01x+1\lt0.01$
$\textbf{Solve the inequality shown above:}$
$-0.01\lt0.01x+1\lt0.01$
Subtract $1$ from all three parts of the inequality:
$-0.01-1\lt0.01x+1-1\lt0.01-1$
$-1.01\lt0.01x\lt-0.99$
Divide all three parts of the inequality by $0.01$:
$-\dfrac{1.01}{0.01}\lt\dfrac{0.01x}{0.01}\lt-\dfrac{0.99}{0.01}$
$-101\lt x\lt-99$
Expressing the solution in interval notation:
$(-101,-99)$