Ii) 1/2(x + 1.7) - 1/3(x – 2.3) = 1

1.	Ii) 1/2(x + 1.7) - 1/3(x – 2.3) = 1
Answer» ANSWER: The value of x is 1.3. Step-by-step-explanation: We have given a linear EQUATION in variable x. We have to find the value of x. The given linear equation is $\displaystyle{\sf\:\dfrac{1}{2}\:(\:x\:-\:1.7\:)\:-\:\dfrac{1}{3}\:(\:x\:-\:2.3\:)\:=\:1}$ $\displaystyle{\implies\sf\:\dfrac{x}{2}\:-\:\dfrac{1.7}{2}\:-\:\left(\:\dfrac{x}{3}\:-\:\dfrac{2.3}{3}\:\right)\:=\:1}$ $\displaystyle{\implies\sf\:\dfrac{x\:-\:1.7}{2}\:-\:\left(\:\dfrac{x\:-\:2.3}{3}\:\right)\:=\:1}$ $\displaystyle{\implies\sf\:\dfrac{x\:-\:1.7}{\cancel{2}}\:\times\:\cancel{6}\:-\:\left(\:\dfrac{x\:-\:2.3}{\cancel{3}}\:\times\:\cancel{6}\:\right)\:=\:1\:\times\:6\:\qquad\:\dots\:[\:Multiplying\:by\:6\:]}$ $\displaystyle{\implies\sf\:(\:x\:-\:1.7\:)\:\times\:3\:-\:(\:x\:-\:2.3\:)\:\times\:2\:=\:6}$ $\displaystyle{\implies\sf\:3x\:-\:5.1\:-\:(\:2x\:-\:4.6\:)\:=\:6}$ $\displaystyle{\implies\sf\:3x\:-\:5.1\:-\:2x\:+\:4.6\:=\:6}$ $\displaystyle{\implies\sf\:3x\:+\:5x\:=\:6\:+\:5.1\:-\:4.6}$ $\displaystyle{\implies\sf\:5x\:=\:6\:+\:5.1\:-\:4.6}$ $\displaystyle{\implies\sf\:10\:\times\:5x\:=\:10\:\times\:(\:6\:+\:5.1\:-\:4.6\:)\:\qquad\:\dots\:[\:Multiplying\:by\:10\:]}$ $\displaystyle{\implies\sf\:50x\:=\:60\:+\:51\:-\:46}$ $\displaystyle{\implies\sf\:50x\:=\:60\:+\:5}$ $\displaystyle{\implies\sf\:50x\:=\:65}$ $\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{65}{50}}}$ $\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{13}{10}}}$ $\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:1.3\:}}}}$

Answer»

ANSWER:

The value of x is 1.3.

Step-by-step-explanation:

We have given a linear EQUATION in variable x.

We have to find the value of x.

The given linear equation is

$\displaystyle{\sf\:\dfrac{1}{2}\:(\:x\:-\:1.7\:)\:-\:\dfrac{1}{3}\:(\:x\:-\:2.3\:)\:=\:1}$

$\displaystyle{\implies\sf\:\dfrac{x}{2}\:-\:\dfrac{1.7}{2}\:-\:\left(\:\dfrac{x}{3}\:-\:\dfrac{2.3}{3}\:\right)\:=\:1}$

$\displaystyle{\implies\sf\:\dfrac{x\:-\:1.7}{2}\:-\:\left(\:\dfrac{x\:-\:2.3}{3}\:\right)\:=\:1}$

$\displaystyle{\implies\sf\:\dfrac{x\:-\:1.7}{\cancel{2}}\:\times\:\cancel{6}\:-\:\left(\:\dfrac{x\:-\:2.3}{\cancel{3}}\:\times\:\cancel{6}\:\right)\:=\:1\:\times\:6\:\qquad\:\dots\:[\:Multiplying\:by\:6\:]}$