$\begin{equation*} \begin{cases} \frac{x - 1}{2} - \frac{x - 3}{3} < 2 &\\ \frac{13x - 1}{2} > 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x - 3 - 2x + 6 < 12 &\\ 13x - 1 > 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x - 2x < 12 + 3 - 6 &\\ 13x > 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x < 9 &\\ x > \frac{1}{13} & \end{cases} \end{equation*}$
$\frac{1}{13} < x < 9$
$x ∈ (\frac{1}{13};9)$

$\begin{equation*} \begin{cases} \frac{3x + 1}{2} < -1 &\\ \frac{x}{2} - 1 < x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x + 1 < -2 &\\ x - 2 < 2x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x < -2 - 1 &\\ x - 2x < 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x < -3 &\\ -x < 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x < -1 &\\ x > -2 & \end{cases} \end{equation*}$
−2 < x < −1
x ∈ (−2;−1)

$\begin{equation*} \begin{cases} 4 - \frac{y - 1}{3} ≥ y &\\ \frac{7y - 1}{8} ≥ 6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 12 - y + 1 ≥ 3y &\\ 7y - 1 ≥ 48 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -y - 3y ≥ -12 - 1 &\\ 7y ≥ 48 + 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -4y ≥ -13 &\\ 7y ≥ 49 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y ≤ 3,25 &\\ y ≥ 7 & \end{cases} \end{equation*}$
y ∈ ∅
нет решений

$\begin{equation*} \begin{cases} \frac{5a + 8}{3} - a ≥ 2a &\\ 1 - \frac{6 - 15a}{4} ≥ a & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5a + 8 - 3a ≥ 6a &\\ 4 - 6 + 15a ≥ 4a & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5a - 3a - 6a ≥ -8 &\\ 15a - 4a ≥ 6 - 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -4a ≥ -8 &\\ 11a ≥ 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} a ≤ 2 &\\ a ≥ \frac{2}{11} & \end{cases} \end{equation*}$
$\frac{2}{11} ≤ a ≤ 2$
$a ∈ [\frac{2}{11};2]$