\( \frac { 2 x + a } { a } - 1 < \frac { x + 2 a } { 2 a } + 2 \)

Let's solve the inequality step-by-step! First, we can simplify each side: Starting with the left side: \[ \frac { 2 x + a } { a } - 1 = \frac { 2 x + a - a } { a } = \frac { 2 x } { a } \] Now simplifying the right side: \[ \frac { x + 2 a } { 2 a } + 2 = \frac { x + 2 a } { 2 a } + \frac { 4 a } { 2 a } = \frac { x + 6 a } { 2 a } \] Now we can write the inequality as: \[ \frac { 2 x } { a } < \frac { x + 6 a } { 2 a } \] To eliminate the fractions, we can multiply both sides by \( 2a \) (assuming \( a > 0 \)): \[ 4x < x + 6 a \] Now, subtract \( x \) from both sides: \[ 3x < 6a \] Finally, divide by 3: \[ x < 2a \] So, the solution to the inequality is: \[ x < 2a \]