Question

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

Answer 1

The solution is:

`-(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.

Explanation:

Given the inequality

`-(1)/(2)x\ge 4`

Let us solve the inequality

`-(1)/(2)x\ge 4`

Multiply both sides by -1 (reverse the inequality)

`\left(-(1)/(2)x\right)\left(-1\right)\le \:4\left(-1\right)`

Simplify

`(1)/(2)x\le \:-4`

Multiply both sides by 2

`2\cdot (1)/(2)x\le \:2\left(-4\right)`

Simplify

`x\le \:-8`

Thus, the solution is:

`-(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.