Precalculus: Mathematics for Calculus, 7th Edition

$$\frac{2x+6}{x-2}\lt0$$
Step 1: Decompose our inequality into two functions: $$(2x+6)\times\frac{1}{x-2}\lt0$$ Step 2: We know that like the product of two numbers, let say: $a\times b=0$, then a=0 or b=0 Step 3: From step 2, we have: $$(2x+6)\lt0$$ or $$\frac{1}{x-2}\lt0$$ Step 4: We ready to solve each in inequality: a) 2x+6<0 given b) 2x