Question

solve the equation x/2+x/3=1/6​

Answer 1

Given:-

• $\sf \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{1}{6}$

To find:-

• The value of x

Answer:-

Given that,

$\sf \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{1}{6}$

$\sf \longrightarrow \dfrac{3x + 2x}{6} = \dfrac{1}{6}$

$\sf \longrightarrow \dfrac{5x}{6} = \dfrac{1}{6}$

$\sf \longrightarrow 6(5x) = 6(1)$

$\sf \longrightarrow \cancel{ 6}(5x) = \cancel{6}(1)$

$\sf \longrightarrow 5x = 1$

$\longrightarrow \underline{ \underline{ \sf{ \green{ x = \dfrac{1}{5} }}}}$

Verify:

L.H.S.:

$\sf \dfrac{x}{2} + \dfrac{x}{3}$

Putting x = 1/5,

$\sf = \dfrac{ \: \: \bigg( \dfrac{1}{5} \bigg) \: \: }{2} + \dfrac{ \: \: \bigg( \dfrac{1}{5} \bigg) \: \: }{3}$

$\sf = \dfrac{1}{5 \times 2} + \dfrac{1}{5 \times 3}$

$\sf = \dfrac{1}{10} + \dfrac{1}{15}$

$\sf = \dfrac{3 + 2}{30}$

$\sf = \dfrac{5}{30}$

$\sf = \dfrac{1}{6}$

R.H.S.:

$\sf \dfrac{1}{6}$

Hence verified!