Question

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

Answer 1

Answer:

The solution is:

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

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

$\frac{3}{4}\:x\:-\:\frac{2}{3}\:\:\le \frac{5}{6}\:$

Add 2/3 to both sides

$\frac{3}{4}x-\frac{2}{3}+\frac{2}{3}\le \frac{5}{6}+\frac{2}{3}$

Simplify

$\frac{3}{4}x\le \frac{3}{2}$

Multiply both sides by 4

$4\cdot \frac{3}{4}x\le \frac{3\cdot \:4}{2}$

$3x\le \:6$

divide both sides by 3

$\frac{3x}{3}\le \frac{6}{3}$

Simplify

$x\le \:2$

Therefore, the solution is:

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

The solution graph is also attached.