ORQ-Nicole,+Kris,+Adi

__** 5/x < 3x+5 **__ **1.** Functions: **y=5/x** and **y=3x+5**.

**2.** The function y=5/x has a domain that is not all real numbers, because it will not cross the y-axis, where x=0. It's domain would be all real numbers except for 0, or x>0 or x<0. We know that these functions will intersect at least once because y=5/x is an inverse function in the first and third quadrants, and y=3x+5 is a linear function with a positive slope, so they will intersect twice. Also, we came up with these functions on our own. 4.
 * 3. ** 5/x < 3x+5

**5. 3x+5>5/x**  **x(3x+5)>5**   **3x^2+5x>5**   **3x^2+5x-5 **  **(Quadratic Formula v) { = radical sign of all inside** **-b+/-{b^2-4(a)(c)}/2a ** **-5+/-{5^2-4(3)(-5)}/2(3)** **-5+/-{25+60}/6** **-5+/-{85}/6** **-5+/-9.22/6** **-5+9.22/6=x -5-9.22/6=x** **x=0.70 x=-2.37** **(using 5/x from original inequality)** **5/.7=y 5/-2.37=y** y=7.1 y=-2.11

(0.70, 7.1) (-2.37, -2.11)

**6. 3x+5> 5/x** -2.37oked at the graph to see where the function y=5/x w as less than y=3x+5 to solve the inequality.