Solve the rational inequality Write the solution set in inte

Solve the rational inequality. Write the solution set in interval notation. X - 7/x + 8 less than or equal to 0

Solution

(x – 7)/(x + 8) 0

When x = 7, we have (x – 7)/(x + 8) = 0 When x > 7 , (x – 7)/(x + 8) > 0

When x = - 8 , (x – 7)/(x + 8) is undefined. When - 8 < x < 7, the denominator is positive and the numerator is negative so that (x – 7)/(x + 8) < 0. When x < - 8 , both the numerator and the numerator are negative so that (x – 7)/(x + 8) > 0 . Thus the solution of the given inequality is - 8 < x 7 i.e. ( -8 , 7]