Solve |2x + 1| > 7: Absolute Value Inequality Challenge

Given:

$|2x + 1| > 7$

Which of the following statements is necessarily true?

To solve the inequality $|2x + 1| > 7$, we split it into two separate inequalities:

$2x + 1 > 7$ or $2x + 1 < -7$.

For the first inequality $2x + 1 > 7$, subtract 1 from both sides:

$2x > 6$

Divide by 2:

$x > 3$

For the second inequality $2x + 1 < -7$, subtract 1 from both sides:

$2x < -8$

Divide by 2:

$x < -4$

Therefore, the solution is $x > 3$ or $x < -4$.