> [!summary] The squeeze theorem justifies why a value $x$ confined between an inequality equal to a value. > **Key Equations:** > **Squeeze Theorem:** > $ \text{If $a=b$ and $x$ is unknown then if } a\leq x \leq b \text{ then $x=a=b$} > $ >[!info]+ Read Time **⏱ 1 min** # Definition The squeeze theorem uses the definition of inequalities to justify why a value between two inequalities equates to some value. So if $a=b$ and we want to know the value of $x$ then if $a\leq x\leq b$, then $x$ must be equal to $x=a=b$. This is true because $a=b$ and because $x$ is confined between the two $x=a=b$. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/2attRllfd-g?si=_9cLL9MiqlzfuurM" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>