Inequalities
- Tags
- math
An inequality is an expression that expresses a relation between two numbers.
For example
Warn: When multiplying an inequality by a negative sign, you must reverse the
direction of the inequality. For example
Solving Quadratic Inequalities
You may sometimes be asked to find the range of values for which a formula, such
as a quadratic equation, is within some range.
For example find the values of
To do so you must first solve the quadratic and find its real valued roots, in
this case
Using a Plot
\begin{figure}
\centering
\begin{tikzpicture}
\begin{axis}[axis lines=center, domain=-10:10]
\addplot[color=red]{x^2 - 4*x - 5};,
\addplot[only marks] coordinates {(-1, 0) (5, 0)};,
\end{axis}
\end{tikzpicture}
\caption{Plot of equation \autoref{eq:quadratic-inequality-eg}}
\label{fig:quadratic-inequality-eg}
\end{figure}
In fig:quadratic-inequality-eg we see that the curve dips below
Using a Number Line
Alternatively we could've created a number-line and substituted in values for
\begin{table}[] \centering \begin{tabular}{c|ll|lllll|ll}
Sign & \multicolumn{2}{c|}{+ve} & \multicolumn{5}{c|}{-ve} & \multicolumn{2}{c}{+ve} \\\\
\hline
x & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\\\
y & 7 & & -5 & & & & & & 7
\end{tabular} \label{tbl:quadratic-inequality-eg} \caption{Number line showing how the value of $y$ changes across the x-axis intersections.} \end{table}
In tbl:quadratic-inequality-eg we see that at