Solve a system of linear inequalities Algebra I

Solve the following system of linear inequalities.

\begin{cases} 2x+3 \lt 1 \cr \cr 4-x≥3 \end{cases}

x \lt -5

x \lt 3

x \lt -1

x \lt -2

\begin{cases} 2x+4 \lt 10 \cr \cr 4-2x≥6 \end{cases}

-7\leq x \lt 4

-6\leq x

x \leq -1

-9\leq x \lt -4

\begin{cases} x+4 \lt 8 \cr \cr 2-x≥5 \end{cases}

-5\leq x \lt 4

x \leq -3

-2\leq x \lt 5

-5\leq x

\begin{cases} 2x \lt 12 \cr \cr -x≥7 \end{cases}

x \leq -7

-9\leq x \lt 14

x \lt 14

-5\leq x \lt 4

\begin{cases} 4x+8 \lt 24 \cr \cr 2-2x≥14 \end{cases}

-5\leq x

-5\leq x \lt 4

-1\leq x \lt 3

x \leq -6

\begin{cases} 3x+6 \lt 18 \cr \cr 4-4x\leq24 \end{cases}

-1\leq x \lt 7

x \lt 3

-3\leq x

-5\leq x \lt 4

\begin{cases} -3x+3 \gt 18 \cr \cr 10+4x≥12 \end{cases}

x \geq \dfrac{5}{3}

x \geq \dfrac{12}{5}

x \geq \dfrac{1}{2}

x \leq \dfrac{-1}{2}