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NSW Y12 Maths - Advanced Graphs and Equations Solving Inequations

Resources for Solving Inequations

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Solving Inequations Theory

It is important to be able to solve quadratic and absolute value inequalities.\\ \begin{multicols}{2} \textbf{Example 1}\\ Solve \(2 x^2+7 x-4 \leq 0\)\\ \textbf{Example 1 solution}\\ \((2 x-1)(x+4) \leq 0\)\\ \begin{center} \resizebox{3in}{!}{ \begin{tikzpicture} \def \xnegative{-6} %negative x value range \def \xpositive{3} %positive x value range \def \xy{\x} %label x or y or any alphabet \draw[latex-latex,line width=0.5mm] (\xnegative.5,0) -- (\xpositive.5,0) node[right] {\Large\(x\)}; \foreach \x in {\xnegative,...,\xpositive} \draw[thin] (\x,4pt )--(\x, -4pt ) node[below=3pt]{\Large\(\xy\)}; \draw[line width=2pt,fill=black] (-4,0) circle (0.2); \draw[line width=2pt,fill=black] (0.5,0) circle (0.2) node[below=4pt] {\LARGE \(\frac{1}{2}\)}; \node[red] at (-5,0.5) {\LARGE\(+\)}; \node[red] at (-5.5,0.5) {\LARGE\(+\)}; \node[red] at (-1.5,-1.2) {\LARGE\(-\)}; \node[red] at (-0.5,-1.2) {\LARGE\(-\)}; \node[red] at (-2.5,-1.2) {\LARGE\(-\)}; \node[red] at (-3.5,-1.2) {\LARGE\(-\)}; \node[red] at (2.5,0.5) {\LARGE\(+\)}; \node[red] at (1.5,0.5) {\LARGE\(+\)}; \end{tikzpicture} } %\includegraphics[width=0.3\textwidth]{Screenshot 2022-12-23 153116} \end{center} \(\therefore-4 \leq x \leq \dfrac{1}{2}\)\\ \columnbreak \textbf{Example 2}\\ Solve \(|2 x-1|<7\)\\ \textbf{Example 2 solution}\\ $\begin{aligned} -7&<2 x-1<7 \\ -6&<2 x<8 \\ -3&<x<4 \end{aligned}$\\ \end{multicols}

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Videos

Videos relating to Solving Inequations.

  • Solving Inequations - Video - Solving Quadratic Inequalities

  • Solving Inequations - Video - Absolute Value Inequalities - How To Solve It

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