Question

(viii)
3/5(x-4) - 1/3 (2x - 9) = 1 / 4(x - 1)-2
​

Answer 1

I hope you got the answer of this question. ....

Answer 2

Answer:

The value of x is

$\displaystyle{\boxed{\red{\sf\:x\:=\:9}}}$

Step-by-step-explanation:

We have given a linear equation with variable x.

We have to find the value of x.

The given equation is

$\displaystyle{\sf\:\dfrac{3}{5}\:(\:x\:-\:4\:)\:-\:\dfrac{1}{3}\:(\:2x\:-\:9\:)\:=\:\dfrac{1}{4}\:(\:x\:-\:1\:)\:-\:2}$

$\displaystyle{\implies\sf\:\dfrac{3x}{5}\:-\:\dfrac{12}{5}\:-\:\left(\:\dfrac{2x}{3}\:-\:\dfrac{9}{3}\:\right)\:=\:\dfrac{x}{4}\:-\:\dfrac{1}{4}\:-\:2}$

$\displaystyle{\implies\sf\:\dfrac{3x\:-\:12}{5}\:-\:\left(\:\dfrac{2x\:-\:9}{3}\:\right)\:=\:\dfrac{x\:-\:1}{4}\:-\:2}$

$\displaystyle{\implies\sf\:\dfrac{3x\:-\:12}{5}\:-\:\left(\:\dfrac{2x\:-\:9}{3}\:\right)\:=\:\dfrac{x\:-\:1\:-\:8}{4}}$

$\displaystyle{\implies\sf\:\dfrac{3x\:-\:12}{5}\:-\:\left(\:\dfrac{2x\:-\:9}{3}\:\right)\:=\:\dfrac{x\:-\:9}{4}}$

$\displaystyle{\implies}\sf\:\dfrac{(\:3x\:-\:12\:)\:\times\:\cancel{60}}{\cancel{5}}\:-\:\left(\:\dfrac{(\:2x\:-\:9\:)\:\times\:\cancel{60}}{\cancel{3}}\:\right)\:=\:\dfrac{(\:x\:-\:9\:)\:\times\:\cancel{60}}{\cancel{4}}\:\:\dots\:[\:Multiplying\:by\:60\:]$

$\displaystyle{\implies\sf\:12\:\times\:(\:3x\:-\:12\:)\:-\:(\:2x\:-\:9\:)\:\times\:20\:=\:15\:\times\:(\:x\:-\:9\:)}$

$\displaystyle{\implies\sf\:36x\:-\:144\:-\:(\:40x\:-\:180\:)\:=\:15x\:-\:135}$

$\displaystyle{\implies\sf\:36x\:-\:144\:-\:40x\:+\:180\:=\:15x\:-\:135}$

$\displaystyle{\implies\sf\:36x\:-\:40x\:-\:15x\:=\:-\:135\:+\:144\:-\:180}$

$\displaystyle{\implies\sf\:-\:4x\:-\:15x\:=\:9\:-\:180}$

$\displaystyle{\implies\sf\:\cancel{-}\:19x\:=\:\cancel{-}\:171}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{171}{19}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:9}}}}$