Solve the nonlinear inequality Express the solution using in

Solve the nonlinear inequality. Express the solution using interval notation (x 8)(x 7)(x 6) 0 Graph the solution set. Use the tools to enter your answer. 10 WebAssign. Numberl ine Need Help? Read It 10 NO SOL Help

Solution

( x - 8 ) ( x-7 ) ( x+6 ) > 0

dividing the number line into 3 intervals

---------- - 6 --------------- 7 ----------8--------------

testing the inequality at each interval

first test point is -7

( -7 - 8 ) ( -7-7 ) ( -7+6 ) > 0

(-15)(-14)(-1) >0

false

2nd point 0

( 0 - 8 ) ( 0-7 ) ( 0+6 ) > 0

(-8)(-7)(+6) >0

true

3rd test point (7.5)

( 7.5 - 8 ) ( 7.5-7 ) ( 7.5+6 ) > 0

false

( x - 8 ) ( x-7 ) ( x+6 ) > 0

test point 9

( 9 - 8 ) ( 9-7 ) ( 9+6 ) > 0

true

hence , solution is

(-6,7) U ( 8 , infinity )