Question

$\frac{x - 1}{2 } = 2 - \frac{x}{3}$
find the value of x​

Answer 1

Answer:

Hope it helps you!!!!!!

Answer 2

Solution:

Given expression:

$\sf{\implies\:\dfrac{x-1}{2}=2-\dfrac{x}{3}}$

Solving procedure:

First we need to include the whole number 2 in the fraction in the RHS. Here the steps are:

$\sf{\longrightarrow\:\dfrac{x-1}{2}=\dfrac{2}{1}\times\dfrac{3}{3}-\dfrac{x}{3}}$

$\sf{\longrightarrow\:\dfrac{x-1}{2}=\dfrac{6}{3}-\dfrac{x}{3}}$

$\sf{\longrightarrow\:\dfrac{x-1}{2}=\dfrac{6-x}{3}}$

Doing cross-multiplication:

$\sf{\longrightarrow\:3(x-1)=2(6-x)}$

$\sf{\longrightarrow\:3x-3=12-2x}$

$\sf{\longrightarrow\:3x+2x=12+3}$

$\sf{\longrightarrow\:5x=15}$

$\sf{\longrightarrow\:x=\dfrac{15}{5}}$

$\sf{\longrightarrow\:x=3}$

Henceforth the value of x is 3.

⇒ Verification:

LHS:

$\sf{\maltese\:\:\dfrac{x-1}{2}}\:where\:the\:value\:of\:x\:is\:3.$

$\sf{=\dfrac{3-1}{2}}$

$\sf{=\dfrac{2}{2}}$

$\sf{=1}$

RHS:

$\sf{\maltese\:\:2-\dfrac{x}{3}\:where\:x\:is\:3.}$

$\sf{=2-\dfrac{3}{3}}$

$\sf{=2-1}$

$\sf{=1}$

LHS = RHS

Hence verified!