Question

(x - 7 )/3 = (x - 1)/5

Answer 1

Answer :-

$\hookrightarrow\sf \dfrac{x - 7}{3} = \dfrac{x - 1}{5}$

By cross multiplication,

$\hookrightarrow\sf5 \: (x - 7) = 3 \: (x - 1)$

Removing the brackets,

$\hookrightarrow\sf5x - 35 = 3x - 3$

Putting the constant and variable terms on different sides by the method of transposition,

$\hookrightarrow\sf5x - 3x = - 3 + 35$

On simplifying,

$\hookrightarrow\sf2x = 32$

Transposing 2 from LHS to RHS, changing it's sign,

$\hookrightarrow\sf x = \dfrac{32}{2}$

Dividing 32 by 2,

$\hookrightarrow \underline{\boxed{\sf x = 16}}$

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

• To check our answer, let's put 16 in the place of x and see whether LHS = RHS.

LHS

$\leadsto \rm\dfrac{x - 7}{3}$

Substituting the value of x,

$\leadsto\rm\dfrac{16 - 7}{3}$

Subtracting 7 from 16,

$\leadsto\rm \dfrac{9}{3}$

Dividing 9 by 3,

$\leadsto\rm3$

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RHS

$\leadsto\rm\dfrac{x - 1}{5}$

Substituting the value of x,

$\leadsto\rm\dfrac{16 - 1}{5}$

Subtracting 1 from 16,

$\leadsto\rm \dfrac{15}{5}$

Dividing 15 by 5,

$\leadsto\rm3$

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LHS = RHS.

Hence verified!