Question

3/4 x - 2/3 less than or equal to 5/6

Answer 1

The solution is:

`(3)/(4)x-(2)/(3)\le (5)/(6)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}`

The solution graph is also attached.

Explanation:

Given the expression

' 3/4 x - 2/3 less than or equal to 5/6 '.

In inequality, the phrase 'less than or equal' is represented as ' ≤ ''.

Thus, the expression is

`(3)/(4)\:x\:-\:(2)/(3)\:\:\le (5)/(6)\:`

Add 2/3 to both sides

`(3)/(4)x-(2)/(3)+(2)/(3)\le (5)/(6)+(2)/(3)`

Simplify

`(3)/(4)x\le (3)/(2)`

Multiply both sides by 4

`4\cdot (3)/(4)x\le (3\cdot \:4)/(2)`

`3x\le \:6`

divide both sides by 3

`(3x)/(3)\le (6)/(3)`

Simplify

`x\le \:2`

Therefore, the solution is:

`(3)/(4)x-(2)/(3)\le (5)/(6)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}`

The solution graph is also attached.