Solve (x+2)/(2x-6) 0

Here are the solutions to the problems:

1. Solve $\frac{x+2}{2x-6} \ge 0$

To solve this inequality, we first find the critical points where the numerator or denominator is zero.

• Numerator: $x+2 = 0 \implies x = -2$
• Denominator: $2x-6 = 0 \implies 2x = 6 \implies x = 3$

These critical points divide the number line into three intervals: $(-\infty, -2)$, $(-2, 3)$, and $(3, \infty)$. We test a value from each interval:

• Interval $(-\infty, -2)$: Let $x = -3$. $\frac