We are given the equation:

\[
|2x + 3| - 1 = 6
\]

### Step 1: Isolate the absolute value

First, we add \(1\) to both sides of the equation to isolate the absolute value:

\[
|2x + 3| = 7
\]

### Step 2: Remove the absolute value

The absolute value equation \( |A| = B \) translates to two possible equations:

\[
2x + 3 = 7 \quad \text{or} \quad 2x + 3 = -7
\]

### Step 3: Solve both equations

#### For \( 2x + 3 = 7 \):

\[
2x = 7 - 3
\]
\[
2x = 4
\]
\[
x = \frac{4}{2} = 2
\]

#### For \( 2x + 3 = -7 \):

\[
2x = -7 - 3
\]
\[
2x = -10
\]
\[
x = \frac{-10}{2} = -5
\]

### Step 4: Solution

Thus, the solutions are:

\[
x = 2 \quad \text{or} \quad x = -5
\]

Would you like more details on any step?

Here are 5 related questions to explore:
1. How do you solve equations with absolute values and fractions?
2. What happens if the absolute value is set to a negative number?
3. How do you graph absolute value equations?
4. What are the applications of absolute value in real life?
5. Can absolute value equations have no solutions?

**Tip:** When solving absolute value equations, always check if isolating the absolute term leads to negative values on the other side!

Learn how to solve the absolute value equation |2x + 3| - 1 = 6 with a clear, step-by-step explanation. This problem introduces the absolute value concept, including isolating the absolute value and solving linear equations. Suitable for students in Grades 8-10.

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