Question

x+5/x+2=2/3
Please help me ​

Answer 1

Answer :-

• The value of x is -11.

What to do?

• Solve :- x + 5/x + 2 = 2/3.

Step-by-step explanation :-

$\implies\tt\dfrac{x + 5}{x + 2} = \dfrac{2}{3}$

By cross multiplication,

$\implies\tt2 \: (x + 2) = 3 \: (x + 5)$

On simplifying,

$\implies\tt2x + 4 = 3x + 15$

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

$\implies\tt2x - 3x = 15 - 4$

On simplifying,

$\implies\tt - x = 11$

$\implies\tt x = - 11$

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Verification :-

• To check our answer, let's put -11 in the place of x and see whether LHS = RHS.

LHS

$\implies\sf \dfrac{x + 5}{x + 2}$

Substituting the value of x,

$\implies\sf\dfrac{ - 11 + 5}{ - 11 + 2}$

On simplifying,

$\implies\sf \dfrac{ - 6}{ - 9}$

Reducing the fraction to it's simplest form,

$\implies\sf \dfrac{\not \!- 2}{\not\!- 3}$

$\implies\sf\dfrac{2}{3}$

RHS

$\implies \sf\dfrac{2}{3}$

LHS = RHS.

Hence verified!

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