Question

1. Write the solution set in interval notation: 3x-2 > x-4 or 7x-5 < 3x+3

Answer 1

`3x-2>x-4 \hbox{ or } 7x-5<3x+3 \\ \\ 3x-2>x-4 \\ 3x-x>-4+2 \\ 2x>-2 \\ x>(-2)/(2) \\ x>-1 \\ \\ 7x-5<3x+3 \\ 7x-3x<3+5 \\ 4x<8 \\ x<(8)/(4) \\ x<2 \\ \\ x>-1 \hbox{ or } x<2 \\ \boxed{x \in (-\infty,\infty)}`

Answer 2

`3x-2>x-4\ \ | subtract\ x\ \ \ \ \textbf{or}\ \ \ \ 7x-5<3x+3\ \ \ | subtract\ 3x\\\\ 2x-2>-4\ \ | add\ 2\ \ \ \ \ \textbf{or}\ \ \ \ 4x-5<3\ \ \ | add\ 5\\\\ 2x>-2\ \ \ \ \ \textbf{or}\ \ \ \ \ 4x<8\\\\ x>-1\ \ \ \ or\ \ \ \ x<2\\\\ Solution:\ \ x\in (-\infty, +\infty)`