(x+2)/(x+3)=(2x-3)/(3x-7)
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Answers
EXPLANATION.
⇒ (x + 2)/(x + 3) = (2x - 3)/(3x - 7).
As we know that,
We can write equation, we get.
⇒ (x + 2)(3x - 7) = (2x - 3)(x + 3).
⇒ 3x² - 7x + 6x - 14 = 2x² + 6x - 3x - 9.
⇒ 3x² - x - 14 = 2x² + 3x - 9.
⇒ 3x² - 2x² - x - 3x - 14 + 9 = 0.
⇒ x² - 4x - 5 = 0.
Factorizes the equation into middle term splits, we get.
⇒ x² - 5x + x - 5 = 0.
⇒ x(x - 5) + 1(x - 5) = 0.
⇒ (x + 1)(x - 5) = 0.
⇒ x = - 1 and x = 5.
Given : (x+2)/(x+3)=(2x-3)/(3x-7)
To Find : The value of x
Solution : Here, first we'll interchange them to the other sides and then simplify both the sides after which factorising it we will find two different values for x out of which the more appropriate one will be chosen as the answer.
- (x + 2)(3x - 7) = (2x - 3)(x + 3)
Simplifying both the sides
- 3x² - 7x + 6x - 14 = 2x² + 6x - 3x - 9
Simplifying Further..
- 3x² - 2x² - x - 14 = 3x - 9
- x² - x - 3x - 14 + 9 = 0
Transposing everything on the RHS we get 0 on the LHS
- x² - 4x - 5 = 0
Factorising it we get
- x² - (5 - 1)x - 5 = 0
- x² - 5x + x - 5 = 0
Taking common from both
- x(x - 5) + 1(x - 5) = 0
- (x - 5)(x + 1) = 0
Now, according to the rule of quadratic equations we will get two conditions.
1ˢᵗ condition :
x - 5 = 0
As it's -ve so going on to the other side it will become positive. After which we get the value of x as
x = 5
2ⁿᵈ condition :
x + 1 = 0
On the other hand the integer is +ve so going on to the left side it becomes negative. After which the output is
x = -1
So, -ve one is rejected and -ve integer is accepted.
Henceforth, the value of x is 5