Let's break down and clarify the equation you provided to solve it step by step. I believe there might be some ambiguity due to the formatting, so I'll interpret the equation as follows:

$1 + 3 \cdot \left| 2x + 1 \right| = 16$

Where:

• $\left| 2x + 1 \right|$ represents the absolute value of $2x + 1$.

Steps to solve:

1. Start by isolating the absolute value expression:

$3 \cdot \left| 2x + 1 \right| = 16 - 1$ $3 \cdot \left| 2x + 1 \right| = 15$

2. Divide both sides by 3:

$\left| 2x + 1 \right| = \frac{15}{3} = 5$

3. The absolute value equation $\left| 2x + 1 \right| = 5$ gives two possible cases:

   • Case 1: $2x + 1 = 5$
   • Case 2: $2x + 1 = -5$

4. Solve each case:

   • Case 1: $2x + 1 = 5$ Subtract 1 from both sides: $2x = 4$ Divide by 2: $x = 2$

   • Case 2: $2x + 1 = -5$ Subtract 1 from both sides: $2x = -6$ Divide by 2: $x = -3$

Final Answer:

The solutions are $x = 2$ and $x = -3$.

---

Do you want further details on these steps or any clarification?

Here are 5 related questions for practice:

1. Solve $4 + 2 \cdot \left| x - 3 \right| = 10$.
2. Find $x$ in the equation $2\left| x + 1 \right| + 3 = 11$.
3. Solve $\left| 5x - 2 \right| = 8$.
4. What are the solutions for $x$ if $\left| 3x + 4 \right| = 7$?
5. Solve for $x$ in $1 + 2\left| 4x - 1 \right| = 13$.

Tip: When solving absolute value equations, always consider the positive and negative scenarios for the expression inside the absolute value.