Solve the Absolute Value Inequality: |2x - 5| > 7 Step by Step

Solve the inequality:

$|2x - 5| > 7$

To solve $|2x - 5| > 7$, we consider the definition of absolute value inequality $|A| > B$, which means $A > B$ or $A < -B$.

Thus, $2x - 5 > 7$ or $2x - 5 < -7$.

Let's solve these inequalities separately:

1. $2x - 5 > 7$

Add 5 to both sides:

$2x > 12$

Divide by 2:

$x > 6$

2. $2x - 5 < -7$

Add 5 to both sides:

$2x < -2$

Divide by 2:

$x < -1$

Therefore, the solution is $x < -1 \text{ or } x > 6$.