Consider the system of inequalities,
[tex]\begin{gathered} 2x-5\leq3 \\ 3x-1\ge-19 \end{gathered}[/tex]
Simplify the first inequality as follows,
[tex]\begin{gathered} 2x-5+5\leq3+5 \\ 2x\cdot\frac{1}{2}\leq8\cdot\frac{1}{2} \\ x\leq4 \end{gathered}[/tex]
So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.
Simplify the second inequality as follows,
[tex]\begin{gathered} 3x-1+1\ge-19+1 \\ 3x\cdot\frac{1}{3}\ge-18\cdot\frac{1}{3} \\ x\ge-6 \end{gathered}[/tex]
So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.
The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.
The solution can be seen on the number line as follows,
