Question

How do you solve `x^ { 2} + 3x - 11\geq x - 3`?

Answer 1

Bring the inequality to standard form of a quadratic inequality:
`f(x) = x^2 + 2x - 8 >= 0`
First solve f(x) = 0
Find 2 real roots knowing the sum (-b = - 2) and the product
(c = - 8). They are 2 and - 4.
Between the 2 real roots f(x) < 0 because the parabola graph is below the x-axis, as the parabola opens upward (a > 0).
f(x) > 0, out side this interval .
Answers by the 2 half closed intervals (-inf., -4], and [2, +inf.).
The 2 end points 2 and -4 are included in the solution set.
Answer by the number line

++++++++++++ -4 -------------------- 0 ----------- 2 +++++++++++++++