Question

Solve |2X+3|<1
Give your answer using interval notation.

Answer 1

To solve the inequality \(|2X + 3| < 1\), we start by splitting it into two separate inequalities:

\[
-1 < 2X + 3 < 1
\]

Now, we can solve each part of the inequality step by step.

1. Solve the left part of the compound inequality:

\[
-1 < 2X + 3
\]
Subtract 3 from both sides:

\[
-1 - 3 < 2X
\]
\[
-4 < 2X
\]
Now, divide by 2:

\[
-2 < X
\]
or
\[
X > -2
\]

2. Now, solve the right part of the compound inequality:

\[
2X + 3 < 1
\]
Subtract 3 from both sides:

\[
2X < 1 - 3
\]
\[
2X < -2
\]
Now, divide by 2:

\[
X < -1
\]

Putting both parts together, we have:

\[
-2 < X < -1
\]

In interval notation, this solution is represented as:

\[
(-2, -1)
\]

So, the final answer is:

\[
\boxed{(-2, -1)}
\]