How do you solve the inequality #x^2+x-20 >= 0# ?

The answer key says #-5 <= x <= 4#

1 Answer
Sep 1, 2017

Answer:

It seems the answer key was for #x^2+x-20 <= 0#.

The given problem has solution:

#x <= -5# or #x >= 4#

Explanation:

Given:

#x^2+x-20 >= 0#

This factors as:

#(x+5)(x-4) >= 0#

This will hold if any of the following:

  • #(x+5 > 0" "# and #" "x-4 > 0)" "<=>" "x > 4#

  • #(x+5 < 0" "# and #" "x-4 < 0)" "<=>" "x < -5#

  • #x+5 = 0" "<=>" "x = -5#

  • #x-4 = 0" "<=>" "x = 4#

Hence we find the solution set is:

#x in (-oo, -5] uu [4, oo)#

That is:

#x <= -5" "# or #" "x >= 4#

It seems that the answer key was for a different problem, namely:

#x^2+x-20 <= 0#