Answer:
We conclude that:
[tex]-4k+5\le \:21\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
The number line graph of the solution is also attached below.
Step-by-step explanation:
Given the equation
[tex]-4k+5\le \:21[/tex]
Subtract 5 from both sides
[tex]-4k+5-5\le \:21-5[/tex]
Simplify
[tex]-4k\le \:16[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex]\left(-4k\right)\left(-1\right)\ge \:16\left(-1\right)[/tex]
Simplify
[tex]4k\ge \:-16[/tex]
Divide both sides by 4
[tex]\frac{4k}{4}\ge \frac{-16}{4}[/tex]
Simplify
[tex]k\ge \:-4[/tex]
Therefore, we conclude that:
[tex]-4k+5\le \:21\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]
The number line graph of the solution is also attached below.
