Question

The solution of the equation x/4 + x/2 = ⅛ is​

Answer 1

Answer :-

• The solution of the equation x/4 + x/2 = 1/8 is 1/6.

Step-by-step explanation :-

$\longmapsto\sf \dfrac{x}{4} + \dfrac{x}{2} = \dfrac{1}{8}$

Taking the LCM of 2 and 4,

$\longmapsto\sf\dfrac{x \times 1 + x \times 2}{4} = \dfrac{1}{8}$

On simplifying,

$\longmapsto \sf\dfrac{x + 2x}{4} = \dfrac{1}{8}$

Adding 2x to x,

$\longmapsto\sf\dfrac{3x}{4} = \dfrac{1}{8}$

On cross multiplying the fractions,

$\longmapsto\sf8 \: (3x) = 4 \: (1)$

Removing the brackets,

$\longmapsto\sf8 \times 3x = 4 \times 1$

On simplifying,

$\longmapsto\sf24x = 4$

Transposing 24 from LHS to RHS, changing it's sign,

$\longmapsto\sf x = \dfrac{4}{24}$

Reducing 4/24 to it's simplest form,

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

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V E R I F I C A T I O N

• To check our answer, let's put 1/6 in the place of x and see whether LHS = RHS.

LHS

$\longrightarrow\rm \dfrac{x}{4} + \dfrac{x}{2}$

$\longrightarrow \rm \dfrac{ \frac{1}{6} }{4} + \dfrac{ \frac{1}{6} }{2}$

$\longrightarrow\dfrac{1}{6} \times \dfrac{1}{4} + \dfrac{1}{6} \times \dfrac{1}{2}$

$\longrightarrow\rm\dfrac{1}{24} + \dfrac{1}{12}$

$\longrightarrow\dfrac{1 \times 1 + 1 \times 2}{24}$

$\longrightarrow\rm\dfrac{1 + 2}{24}$

$\longrightarrow\dfrac{3}{24}$

$\longrightarrow\dfrac{1}{8}$

RHS

$\longrightarrow\dfrac{1}{8}$

LHS = RHS.

Hence verified!

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