Solve the following equations and verify your answer - x-2-x-5 - x-x-6

X+2/x+5 = x/x+6 By cross multiplication : (x+2)(x+6) = x(x+5) ⇒ x^2 + 6x + 2x + 12 = x^2 + 5x ⇒ x^2 + 8x + 12 = x^2 + 5x ⇒ x^2 + 8x x^2 5x = 12 ⇒ 3x = 12 ...

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Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equations and verify your answer :

$\frac{x + 2}{x + 5} = \frac{x}{x + 6}$

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Solution

$\frac{x + 2}{x + 5} = \frac{x}{x + 6}$
By cross multiplication :
$(x + 2) (x + 6) = x (x + 5) \Rightarrow x^{2} + 6 x + 2 x + 12 = x^{2} + 5 x \Rightarrow x^{2} + 8 x + 12 = x^{2} + 5 x \Rightarrow x^{2} + 8 x - x^{2} - 5 x = - 12 \Rightarrow 3 x = - 12 \Rightarrow x = \frac{- 12}{3} = - 4 ∴ x = - 4$
Verification :
$L . H . S . = \frac{x + 2}{x + 5} = \frac{- 4 + 2}{- 4 + 5} = \frac{- 2}{1} = - 2 R . H . S . = \frac{x}{x + 6} = \frac{- 4}{- 4 + 6} = \frac{- 4}{2} = - 2 ∴ L . H . S . = R . H . S .$

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Solve the following equations and verify your answer : x+2x+5=xx+6

x+2x+5=xx+6 By cross multiplication : (x+2)(x+6)=x(x+5)⇒x2+6x+2x+12=x2+5x⇒x2+8x+12=x2+5x⇒x2+8x−x2−5x=−12⇒3x=−12⇒x=−123=−4∴x=−4 Verification : L.H.S.=x+2x+5=−4+2−4+5=−21=−2R.H.S.=xx+6=−4−4+6=−42=−2∴L.H.S.=R.H.S.

Solve the following equations and verify your answer :

$\frac{x + 2}{x + 5} = \frac{x}{x + 6}$