Negative 3x plus 25 greater than 2x plus 5

Question

express the set using interval notation

Answer 1

 

 3x+25 > 2x + 5

 

 3x + 25 - 2x - 5 > 0

 

 x + 20 > 0

 

 x  > -20

 

 

CHECK:

 

   pick something GREATER than -20, like x=0.   

   3x+25 = 3(0) + 25 = 0 + 25 = 25   > 5 = 5 + 0 = 5 +2(0) = 5+2x

  YES IT WORKS

 

  Now pick something LESS than -20 like -25:

  3(-25) + 25 = -75 + 25 = -50   BUT  2(-25) + 5 = -50 + 5 = -45

  and the statement is FALSE because -50 > -45 is FALSE. So it DOES NOT WORK.

 

 THerefore, our answer is CORRECT.

 

 The interval is (-20, infinity)  (-20, oO)

Answer 2

-3x + 25 > 2x + 5

-5x > -20

x < 4

 

(4,∞)