Question

3x+5/7x+5=2/3
find the value of x ​

Answer 1

Answer :-

$Q) \: \sf\dfrac{3x + 5}{7x + 5} = \dfrac{2}{3}$

By cross multiplication,

$\Rightarrow\sf2 \: (7x + 5) = 3 \: (3x + 5)$

Removing the brackets by multiplying the numbers outside the brackets with the numbers inside the brackets,

$\Rightarrow\sf14x + 10 = 9x + 15$

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

$\Rightarrow\sf14x - 9x = 15 - 10$

On simplifying,

$\Rightarrow\sf5x = 5$

Transposing 5 from LHS to RHS, changing it's sign,

$\Rightarrow\sf x = \dfrac{5}{5}$

Dividing 5 by 5,

$\Rightarrow \underline{\boxed{\sf x = 1}}$

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

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

LHS

$\longmapsto\rm\dfrac{3x + 5}{7x + 5}$

Substituting the value of x,

$\longmapsto \rm\dfrac{3 \times 1 + 5}{7 \times 1 + 5}$

Applying the BODMAS rule and multiplying the numbers first,

$\longmapsto\rm \dfrac{3 + 5}{7 + 5}$

Adding the numbers,

$\longmapsto\rm \dfrac{8}{12}$

Reducing the fraction to it's simplest form,

$\longmapsto \rm\dfrac{2}{3}$

RHS

$\longmapsto\rm\dfrac{2}{3}$

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Since LHS = RHS,

Hence verified!