Answer to Question #236772 in Algebra for CCW

Question

Polynomial Inequalities:

1) (x-5) (x+2) < 0

show your number line and state your answer in interval notation

Answer 1

$(x-5)(x+2) < 0\\ \text{The solutions to the inequality is x < -2, -2 <x < 5 and x > 5}\\ \text{We get the solution to the question using the table below}\\ \begin{matrix} & x < -2 & -2 < x < 5 & x > 5\\ x-5 &- &- &+\\ x+2 &- &+ & +\\ (x+5)(x+2) &+ &- & + \end{matrix}\\ \text{Therefore we have that the solution is -2 < x < 5, and the number line is}\\ \text{\quad\quad \quad o------------------o\quad } \\ \text{<--------|------------------|------------>} \\ \text{\quad \quad\quad-2 \quad \quad \quad \quad \quad 5 }\\ \text{The solution in interval form is}\\ x \in (-2, 5)$