Question

3/4(7x-1/4)-(2x-1-x/2)=x+11​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:x\:=\:\dfrac{49}{11}}}}$

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

$\displaystyle{\sf\:\dfrac{3}{4}\:\left(\:7x\:-\:\dfrac{1}{4}\:\right)\:-\:\left(\:2x\:-\:1\:-\:\dfrac{x}{2}\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{21x}{4}\:-\:\dfrac{3}{16}\:-\:\left(\:2x\:-\:\dfrac{x}{2}\:-\:1\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{21x}{4}\:-\:\dfrac{3}{16}\:-\:\left(\:\dfrac{4x\:-\:x}{2}\:-\:1\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{21x\:\times\:4}{4\:\times\:4}\:-\:\dfrac{3}{16}\:-\:\left(\:\dfrac{3x\:-\:2}{2}\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{84x}{16}\:-\:\dfrac{3}{16}\:-\:\left(\:\dfrac{3x\:-\:2}{2}\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{84x\:-\:3}{16}\:-\:\dfrac{8\:\times\:(\:3x\:-\:2\:)}{2\:\times\:8}\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{84x\:-\:3}{16}\:-\:\left(\:\dfrac{24x\:-\:16}{16}\:\right)\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:\dfrac{84x\:-\:36\:-\:(\:24x\:-\:16\:)}{16}\:=\:x\:+\:11}$

$\displaystyle{\implies\sf\:84x\:-\:36\:-\:24x\:+\:16\:=\:(\:x\:+\:11\:)\:\times\:16}$

$\displaystyle{\implies\sf\:84x\:-\:24x\:-\:36\:+\:16\:=\:16x\:+\:176}$

$\displaystyle{\implies\sf\:60x\:-\:20\:=\:16x\:+\:176}$

$\displaystyle{\implies\sf\:60x\:-\:16x\:=\:176\:+\:20}$

$\displaystyle{\implies\sf\:44x\:=\:196}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{196}{44}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:\dfrac{49}{11}}}}}$