Solve |2x + 1| > 3: Absolute Value Inequality Step-by-Step

Given:

$\left|2x + 1\right| > 3$

Which of the following statements is necessarily true?

To solve $\left| 2x + 1 \right| > 3$, consider the two cases for the absolute value: $2x + 1 > 3$ and $2x + 1 < -3$.

1. Solving $2x + 1 > 3$:

$2x + 1 > 3$

Subtract 1 from both sides:

$2x > 2$

Divide both sides by 2:

$x > 1$

2. Solving $2x + 1 < -3$:

$2x + 1 < -3$

Subtract 1 from both sides:

$2x < -4$

Divide both sides by 2:

$x < -2$

Thus, the solution is$x < -2 \text{ or } x > 1$.