College Algebra, Chapter 1, 1.6, Section 1.6, Problem 42

Solve the nonlinear inequality $\displaystyle x^2 < x + 2$. Express the solution using interval notation and graph the solution set.


$
\begin{equation}
\begin{aligned}

& x^2 < x + 2
&& \text{Given}
\\
\\
& x^2 - x - 2 < 0
&& \text{Subtract $x$ and $2$}
\\
\\
&(x -2)(x + 1) < 0
&& \text{Factor}

\end{aligned}
\end{equation}
$


The factors on the left hand side are $x - 2$ and $x + 1$. These factors are zero when $x$ is $2$ and $-1$ respectively. These numbers divide the real line into intervals

$(- \infty, -1), (-1, 2), (2, \infty)$







From the diagram, the solution of the inequality $x^2 < x + 2$ is