Question

Solve each inequality.
1. |2x - 3| /leq 11

Answer 1

To solve the inequality \(\left| 2x - 3 \right| \leq 11\), we can break it down into two separate inequalities:

1. \(2x - 3 \leq 11\)
2. \(2x - 3 \geq -11\)

Let's solve each inequality step by step.

### 1. Solve \(2x - 3 \leq 11\)

Add 3 to both sides:

\[
2x \leq 11 + 3
\]
\[
2x \leq 14
\]

Now, divide both sides by 2:

\[
x \leq 7
\]

### 2. Solve \(2x - 3 \geq -11\)

Add 3 to both sides:

\[
2x \geq -11 + 3
\]
\[
2x \geq -8
\]

Now, divide both sides by 2:

\[
x \geq -4
\]

### Combining the Results

Now we combine the results from both inequalities:

\[
-4 \leq x \leq 7
\]

In interval notation, the solution is:

\[
[-4, 7]
\]