Answer:
The solution is:
[tex]-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}[/tex]
The number line graph of the solution is also attached below.
From the graph, it is clear that the 2nd number line represents the solution set for the inequality.
Step-by-step explanation:
Given the inequality
[tex]-\frac{1}{2}x\ge 4[/tex]
Let us solve the inequality
[tex]-\frac{1}{2}x\ge 4[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex]\left(-\frac{1}{2}x\right)\left(-1\right)\le \:4\left(-1\right)[/tex]
Simplify
[tex]\frac{1}{2}x\le \:-4[/tex]
Multiply both sides by 2
[tex]2\cdot \frac{1}{2}x\le \:2\left(-4\right)[/tex]
Simplify
[tex]x\le \:-8[/tex]
Thus, the solution is:
[tex]-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}[/tex]
The number line graph of the solution is also attached below.
From the graph, it is clear that the 2nd number line represents the solution set for the inequality.
