Question

Q:-x / 2x - 2 = x+5 / 2x + 6
solve this linear equation
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Answer 1

Step-by-step explanation:

$\red{\bold{\underline{\underline{Question᎓}}}}$

Q:-x / 2x - 2 = x+5 / 2x + 6

solve the following linear equation.

$\huge\tt\underline\blue{Answer </p><p> }$

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

$⟹x(2x + 6) = (2x - 2)(x + 5)$

$⟹2 {x}^{2} + 6x = 2x(x + 5) - 2(x + 5)$

$⟹2 {x}^{2} + 6x = 2 {x}^{2} + 10x - 2x - 10$

$⟹2 {x}^{2} + 6x = 2 {x}^{2} + 8x - 10$

$⟹8x - 6x - 10 = 0$

$⟹2x = 10$

$⟹x = \frac{10}{2} = 5$✓

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HOPE IT HELPS YOU..

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Thankyou:)

Answer 2

Working out:

In this question, we are provided with a equation with variable x and we have to solve for x.

GiveN:

• $\sf{ \dfrac{x}{2x - 2} = \dfrac{x + 5}{2x + 6} }$

So let's start solving the equation and understand the steps to get our final result for x.....

$\sf{ \longrightarrow{ \dfrac{x}{2x- 2} = \dfrac{x + 5}{2x + 6} }}$

Cross multiplying the equation,

$\sf{ \longrightarrow{x(2x + 6) = (2x - 2)(x + 5)}}$

Now opening the parentheses and doing the respective calculations (Like multiplication in RHS),

$\sf{ \longrightarrow{2 {x}^{2} + 6x = 2 {x}^{2} + 10x - 2x - 10}}$

Combining the constant and like terms to solve further,

$\sf{ \longrightarrow{2 {x}^{2} + 6x = 2 {x}^{2} + 8x - 10}}$

Now we can see that 2x² in the both sides of the equation, so we can subtract from both sides,

$\sf{ \longrightarrow{6x = 8x - 10}}$

We have to find x, so let's isolate it in one side of the equation,

$\sf{ \longrightarrow{6x - 8x = - 10}}$

$\sf{ \longrightarrow{ - 2x = - 10}}$

Inverse of multiplication is division, so dividing -2 from both sides of the equation,

$\sf{ \longrightarrow{ \dfrac{ - 2x}{ - 2} = \dfrac{ - 10}{ - 2} }}$

$\sf{ \longrightarrow{x = 5}}$

So, the required value for x in the equation is:

$\huge{ \boxed{ \sf{ \purple{x = 5}}}}$

And we are done !!