Given the inequalities:
[tex]\begin{gathered} \frac{x}{4}\ge-1\rightarrow(1) \\ -4x-4\le-3\rightarrow(2) \end{gathered}[/tex]
The solution to the first inequality:
[tex]\begin{gathered} \frac{x}{4}\ge-1\rightarrow\times4 \\ x\ge-4 \\ x\in\lbrack-4,\infty) \end{gathered}[/tex]
The solution to the second inequality:
[tex]\begin{gathered} -4x-4\le-3 \\ -4x\le-3+4 \\ -4x\le1\rightarrow\div(-4) \\ x\ge-\frac{1}{4} \\ x\in\lbrack-\frac{1}{4},\infty) \end{gathered}[/tex]
We will find the intersection between the intervals
So, the answer will be:
[tex]\lbrack-\frac{1}{4},\infty)[/tex]
