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Question

Solve: $$3+\dfrac { x }{ 4 } =\dfrac { 1 }{ 2 } \left( 4-\dfrac { x }{ 3 }  \right) -\dfrac { 5 }{ 6 } +\dfrac { 1 }{ 3 } \left( 11-\dfrac { x }{ 2 }  \right) $$


A
x=227
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B
x=27
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C
x=2278
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D
None of these
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Solution

The correct option is A $$x=\dfrac { 22 }{ 7 } $$
$$3+\dfrac{x}{4}=\dfrac{1}{2}\left(4-\dfrac{x}{3}\right)-\dfrac{5}{6}+\dfrac{1}{3}\left(11-\dfrac{x}{2}\right)$$

$$\Rightarrow 3+\dfrac{x}{4}=2-\dfrac{x}{6}-\dfrac{5}{6}+\dfrac{11}{3}-\dfrac{x}{6}$$

$$\Rightarrow \dfrac{x}{4}+\dfrac{x}{3}=\dfrac{22-5-6}{6}\Rightarrow \dfrac{7x}{12}=\dfrac{11}{6}$$

$$\boxed{x=\dfrac{22}{7}}$$

Mathematics

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