Question

solve: x/2 + x/3 + x/6 = 3​​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies \dfrac{x}{2} + \dfrac{x}{3} + \dfrac{x}{6} = 3$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Value \: of \: x = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf \implies \dfrac{x}{2} + \dfrac{x}{3} + \dfrac{x}{6} = 3$

Find the common denominator.

$\sf \implies \dfrac{x \times 3}{6} + \dfrac{x \times 2}{6} + \dfrac{x}{6} = 3$

Combine the numerators over common denominator.

$\sf \implies \dfrac{x \times 3 + x \times 2 + x}{6} = 3$

Simplify each term.

$\sf \implies \dfrac{3x + 2x + x}{6} = 3$

$\sf \implies \dfrac{5x + x}{6} = 3$

$\sf \implies \cancel{\dfrac{6 x}{6} } = 3$

$\sf \implies x = 3$

Therefore,

$\sf \implies \underline{ \boxed{ \sf Value \: of \: x \: is \: 3 }}$

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$\bf \underline{ \underline{\maltese\: Verification } }$

To verify the answer just write 3 in place of x.

$\sf \implies \dfrac{x}{2} + \dfrac{x}{3} + \dfrac{x}{6} = 3$

$\sf \implies \dfrac{3}{2} + \dfrac{3}{3} + \dfrac{3}{6} = 3$

Find the common denominator.

$\sf \implies \dfrac{3 \times 3}{6} + \dfrac{3 \times 2}{6} + \dfrac{3}{6} = 3$

$\sf \implies \dfrac{9}{6} + \dfrac{6}{6} + \dfrac{3}{6} = 3$

Combine the numerators over common denominator.

$\sf \implies \dfrac{9 + 6+ 3}{6} = 3$

$\sf \implies \cancel{\dfrac{18}{6} }= 3$

$\sf \implies 3= 3$

LHS and RHS are equal.

$\bold{\longrightarrow} \:\large{\sf \red{Hence\:Verified\:!}}$