Answer:
The solution is:
[tex]\frac{3}{4}x-\frac{2}{3}\le \frac{5}{6}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}[/tex]
The solution graph is also attached.
Step-by-step 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
[tex]\frac{3}{4}\:x\:-\:\frac{2}{3}\:\:\le \frac{5}{6}\:[/tex]
Add 2/3 to both sides
[tex]\frac{3}{4}x-\frac{2}{3}+\frac{2}{3}\le \frac{5}{6}+\frac{2}{3}[/tex]
Simplify
[tex]\frac{3}{4}x\le \frac{3}{2}[/tex]
Multiply both sides by 4
[tex]4\cdot \frac{3}{4}x\le \frac{3\cdot \:4}{2}[/tex]
[tex]3x\le \:6[/tex]
divide both sides by 3
[tex]\frac{3x}{3}\le \frac{6}{3}[/tex]
Simplify
[tex]x\le \:2[/tex]
Therefore, the solution is:
[tex]\frac{3}{4}x-\frac{2}{3}\le \frac{5}{6}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:2]\end{bmatrix}[/tex]
The solution graph is also attached.
