https://file.aiquickdraw.com/mathbot/file/1726755681011lz4nyvcx.jpg

Let's solve both inequalities and express the answers in interval notation as requested.

### (a) \( 1.99 < \frac{1}{x} < 2.01 \)

Step 1: Solve each part of the compound inequality separately.

\[
1.99 < \frac{1}{x}
\]

Multiply both sides by \( x \) (remember to consider the sign of \( x \)):

- If \( x > 0 \), the inequality remains the same:

\[
1.99x < 1
\]
\[
x > \frac{1}{2.01}
\]

- If \( x < 0 \), multiply by \( x \), flipping the inequality:

\[
1.99x > 1 \quad \Rightarrow \quad x < \frac{1}{1.99}
\]

Thus, the solution for this part will be \( x < \frac{1}{2.01} \).

So, this gives a **solution for positive \(x \)** as:  
\( \frac{1}{2.01}

Selesaikan masing-masing pertidaksamaan. Nyatakan penyelesaian anda dalam notasi interval. (a) 1,99 < 1/x < 2,01 (b) 2,99 < 1/(x + 2) < 3,01

Learn how to solve inequalities involving reciprocal functions, such as 1/x and 1/(x+2), with detailed interval notation. This problem helps students understand key algebraic concepts like rational inequalities. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation