Question

x+2/x+5=x/x+6 solve the linear equation and verify

Answer 1

Question:

Solve for the linear equation :

(x+2)/(x+5) = x/(x+6)

and verify it.

Solution:

We have:

=> (x+2)/(x+5) = x/(x+6)

=> (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 + 12 - x^2 - 5x = 0

=> 3x + 12 = 0

=> 3x = -12

=> x = -12/3

=> x = - 4

Thus,

The solution for the given linear equation is : x = - 4.

Verification :

Putting x = - 4 in LHS , we have;

=> LHS = (x+2)/(x+5)

=> LHS = (-4+2)/(-4+5)

=> LHS = -2/1

=> LHS = -2

Now,

Putting x = - 4 in RHS , we have;

=> RHS = x/(x+6)

=> RHS = -4/(-4+6)

=> RHS = -4/2

=> RHS = -2

Since, LHS = RHS , hence verified.

Answer 2

SOLUTION:-

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Given:

x+2/x+5 = x/x+6

To find:

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Solve the linear equation & verify.

Explanation:

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We have,

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

[Cross Multiplication]

$(x + 2)(x + 6) = {x}^{2} + 5x \\ \\ {x}^{2} + 6x + 2x + 12 = {x}^{2} + 5x \\ \\ {x}^{2} + 8x + 12 = {x}^{2} + 5x \\ \\ 8x + 12 = 5x \\ \\ 8x - 5x = - 12 \\ \\ 3x = - 12 \\ \\ x = \frac{ - 12}{3} \\ \\ x = - 4$

Verification:

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Taking L.H.S

$\frac{x + 2}{x + 5} = \frac{x}{x + 6} \\ \\ \frac{ - 4 + 2}{ - 4 + 5} = \frac{ - 4}{ - 4 + 6} \\ \\ \frac{ - 2}{ 1} = \frac{ -4}{2} \\ \\ - 2 = - 2 \: \: \: \: \: \: \: \: [R.H.S]$

:)