Given the inequality:
[tex]-4x+4\leqslant-20[/tex]To solve the inequality for x, the first step is to subtract 4 from both sides of the inequality.
[tex]\begin{gathered} -4x+4-4\leqslant-20-4 \\ -4x\leqslant-24 \end{gathered}[/tex]Next, we divide both sides of the inequality by -4.
Note: When you divide or multiply by a negative number in inequality, the inequality sign reverses.
Therefore, we have:
[tex]\begin{gathered} \frac{-4x}{-4}\geqslant\frac{-24}{-4} \\ x\geqslant6 \end{gathered}[/tex]Next, we write our result in interval notation.
Since the value is greater than or equal to, we use the close bracket '['.
Therefore, the solution to the inequality in interval notation is:
[tex]\lbrack6,\infty)[/tex]