Question

Which graph below represents the solution to the inequality 6 x − 12 − x ≤ 3

Answer 1

The solution is:

`6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}`

The graph of the solution is attached below.

Both the number line and graph is attached below.

Explanation:

Note: you missed to add the graph options. Therefore, I am solving the inequality and adding the corresponding graph which would anyways clear your concept.

Given the inequality expression

`6\:x\:-\:12\:-\:x\:\le \:3`

Group like terms

`6x-x-12\le \:3`

Add similar elements: 6x-x=5x

`5x-12\le \:3`

Add 12 to both sides

`5x-12+12\le \:3+12`

simplify

`5x\le \:15`

Divide both sides by 5

`(5x)/(5)\le (15)/(5)`

simplify

`x\le \:3`

Therefore, the solution is:

`6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}`

• The graph of the solution is attached below.

Both the number line and graph is attached below.