Question

What is the geometric representation of 2/3(3x-5)=2 (2x+1)-11

Answer 1

2x+5=0

let

y=2x+5

Put x=0

y=2×0+5

y=5

x=1

y=2×1+5=7

and x=2

y=2×2+5=9

It is a straight line

Answer 2

Given,

$\[\frac{2}{3}\left( {3x - 5} \right) = 2\left( {2x + 1} \right) - 11\]$

Solution,

$\[\frac{2}{3}\left( {3x - 5} \right) = 2\left( {2x + 1} \right) - 11\]$

$\[\begin{array}{l} \Rightarrow 2\left( {3x - 5} \right) = 6\left( {2x + 1} \right) - 33\\ \Rightarrow 6x - 10 = 12x + 6 - 33\\ \Rightarrow 6x = 17\end{array}\]$

$\[ \Rightarrow x = \frac{{17}}{6}\]$

Hence the represent a line parallel to y-axis.