solve the rational inequality. Express your answer using interval notation. (x-7)/(x+8= 0

Question

solve the rational inequality. Express your answer using interval notation. (x-7)/(x+8≤ 0

Answer 1

(x-7)/(x+8) ≤ 0

 

x - 7 = 0 when x = 7

x + 8 = 0 when x = -8

 

When x < -8, x - 7 < 0 and x + 8 < 0.  So, (x-7)/(x+8) > 0 

 

When -8 < x < 7, x - 7 < 0 and x + 8 > 0.  So, (x-7)/(x+8) < 0

 

When x > 7, x - 7 and x + 8 are both positive.  So, (x-7)/(x+8) > 0

 

(x-7)/(x+8) = 0 when x = 7 and (x-7)/(x+8) is undefined when x = -8

 

Solution:  -8 < x ≤ 7    Interval notation form:  (-8, 7]