Bradley Alexander
09/23/2024 · Elementary School
Solve for \( x \) \( x^{2}-3>2 x \)
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Step-by-step Solution
Solve the equation \( x^{2}-3>2x \).
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
\(x^{2}-3>2x\)
- step1: Move the expression to the left side:
\(x^{2}-3-2x>0\)
- step2: Rewrite the expression:
\(x^{2}-3-2x=0\)
- step3: Factor the expression:
\(\left(x-3\right)\left(x+1\right)=0\)
- step4: Separate into possible cases:
\(\begin{align}&x-3=0\\&x+1=0\end{align}\)
- step5: Solve the equation:
\(\begin{align}&x=3\\&x=-1\end{align}\)
- step6: Determine the test intervals:
\(\begin{align}&x<-1\\&-13\end{align}\)
- step7: Choose a value:
\(\begin{align}&x_{1}=-2\\&x_{2}=1\\&x_{3}=4\end{align}\)
- step8: Test the chosen value:
\(\begin{align}&x<-1\textrm{ }\textrm{is the solution}\\&-13\textrm{ }\textrm{is the solution}\end{align}\)
- step9: The final solution is \(x \in \left(-\infty,-1\right)\cup \left(3,+\infty\right):\)
\(x \in \left(-\infty,-1\right)\cup \left(3,+\infty\right)\)
The solution to the inequality \(x^{2}-3>2x\) is \(x \in (-\infty,-1) \cup (3,+\infty)\).
Quick Answer
\( x \in (-\infty,-1) \cup (3,+\infty) \)
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