Question

Im being timedwhich number line represents the solution set for the inequality?​

Answer 1

Answer:

The solution is:

$-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}$

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

$-\frac{1}{2}x\ge 4$

Let us solve the inequality

$-\frac{1}{2}x\ge 4$

Multiply both sides by -1 (reverse the inequality)

$\left(-\frac{1}{2}x\right)\left(-1\right)\le \:4\left(-1\right)$

Simplify

$\frac{1}{2}x\le \:-4$

Multiply both sides by 2

$2\cdot \frac{1}{2}x\le \:2\left(-4\right)$

Simplify

$x\le \:-8$

Thus, the solution is:

$-\frac{1}{2}x\ge \:4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-8\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-8]\end{bmatrix}$

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.