Question

ii) 1/2(x + 1.7) - 1/3(x – 2.3) = 1​

Answer 1

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 2

Answer:

x =1.3

Step-by-step explanation:

1/2(x + 1.7) - 1/3(x – 2.3) = 1​

$\frac{x - 1.7}{2}$ - $\frac{x - 2.3}{3}$ = 1

(x-1.7) . 3 - (x-2.3) × 2 = 6

3x - 5.1 - 2x + 4.6 = 6

5x = 6 + 5.1 - 4.6

50x = 65

x = $\frac{13}{10}$

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