What is the process behind this? i know multiply by x is the first
2026-03-30 12:01:59.1774872119
Bring x back to the center inequality
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We have \begin{alignat*}{2} x\left(\frac{4}{7}-\epsilon\right) < 4 &\Rightarrow x &&< \frac{4}{\frac{4}{7}-\epsilon} \qquad \text{(assuming $\epsilon < \frac{4}{7}$)} \\ & &&= \frac{7(4)}{7\left(\frac{4}{7}-\epsilon\right)} \\ & &&= \frac{28}{4-7\epsilon}\end{alignat*} and similarly \begin{equation*}x\left(\frac{4}{7}+\epsilon\right) > 4 \Rightarrow x > \frac{28}{4+7\epsilon}\end{equation*} Combining these yields \begin{equation*}\frac{28}{4+7\epsilon} < x < \frac{28}{4-7\epsilon}\end{equation*} as stated.