Question
Solve the inequations: $-8 \leq-(3 x-5)<13$

Answer

$-8<-(3 x-5)<13$ Multiplying by -1 throughout (so inequality sign changes) $8 \geq 3 x-5>-13$ i.e., $-13<3 x-5 \leq 8$
Adding 5 on both the sides, we get
$
-8<3 \mathrm{x} \leq 13
$
Dividing, by 3 on both sides, we get
$
\therefore-\frac{8}{3}<x \leq \frac{13}{3}
$
i.e., $x$ takes all real values between $-\frac{8}{3}$ and $\frac{13}{3}$ including $\frac{13}{3}$.
$\therefore$ the solution set is $\left(-\frac{8}{3}, \frac{13}{3}\right]$

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