Question

solve the inequality. give the solution set using interval notation.
|0.01x + 5| < 0.03

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is .
(simplify your answer. type your answer in interval notation. use integers or decimals for any numbers in the expression.)
b. the solution set is ∅.

Explanation:

Step1: Apply absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), we have \(-b < a < b\). So for \(|0.01x + 5| < 0.03\), we get \(-0.03 < 0.01x + 5 < 0.03\).

Step2: Subtract 5 from all parts

Subtract 5 from each part of the compound inequality: \(-0.03 - 5 < 0.01x + 5 - 5 < 0.03 - 5\), which simplifies to \(-5.03 < 0.01x < -4.97\).

Step3: Divide all parts by 0.01

Divide each part by 0.01: \(\frac{-5.03}{0.01} < \frac{0.01x}{0.01} < \frac{-4.97}{0.01}\), resulting in \(-503 < x < -497\).

Answer:

A. The solution set is \((-503, -497)\)