Solve the Absolute Value Equation: Finding x in |3x + 1| = 4

To solve the absolute value equation $\left|3x + 1\right| = 4$, we set up two separate equations because absolute value represents the distance from zero, meaning the expression inside can be equal to 4 or -4.

1. First equation: $3x + 1 = 4$
2. Subtract 1 from both sides: $3x = 3$
3. Divide both sides by 3: $x = 1$

2. Second equation: $3x + 1 = -4$
3. Subtract 1 from both sides: $3x = -5$
4. Divide both sides by 3: $x = -\frac{5}{3}$

Therefore, the solutions are $x = 1$ and $x = -\frac{5}{3}$, but only the negative solution satisfies the original setup with a valid subtraction and division sequence again as per the equation.