Question

solve the following equation and verify your answer.
$\frac{x {}^{2} - (x + 2)(x + 3) }{7x +1 } \: = \: \frac{2}{3}$
chapter- linear equation in one variable
class 8

go to h e l l mr K I T ​

Answer 1

Answer:

Given Linear equation in one

variable is 7x/2 = 105/2

Multiply both sides by 2, we get

=> (7x/2 ) x 2 = ( 105 )/2

=> 7x = 105

Divide both sides by 7, we get

=> 7x/7 = 105/7

=> x = ( 7 x 15 )/7

=> x = 15

Therefore,

x = 15

Answer 2

Answer:

$\huge\mathfrak\purple{Solution} \:$

$\frac{ {x}^{2} - (x + 2)(x + 3) }{7x + 1} = \frac{2}{3}$

$\frac{ {x}^{2} - [ (x + 2)(x + 3)] }{7x + 1} = \frac{2}{3}$

$\frac{ {x}^{2} - [ \: {x}^{2} + 3x + 2x + 6 \:] }{7x + 1} = \frac{2}{3}$

$\frac{ {x}^{2} - \: [ {x}^{2} + 5x + 6 ]}{7x + 1} = \frac{2}{3}$

$\frac{ {x}^{2} - {x}^{2} - 5x - 6 }{7x + 1} = \frac{2}{3}$

$\frac{ - 5x - - 6}{7x + 1} = \frac{2}{3} = \frac{2}{3}$

By cross Multiplication

3(-5x - 6) = 2(7x + 1)

-15x - 18 = 14x + 2

-15x -14x = 18 + 2

-29x = 20

$x = \frac{ - 20}{29}$

$verification \: for \: x \: = \frac{ - 20}{29}$

$l.h.s = \frac{ - 5x - 6}{7x + 1}$

$= \frac{ - 5( \frac{ - 20}{29} ) - \frac{6}{1} }{7( \frac{ - 20}{29}) + \frac{1}{1} }$

$= \frac{ \frac{100}{29} - \frac{6}{1} }{ \frac{ - 140}{29} + \frac{1}{1} }$

$l.h.s = \frac{ \frac{100 - 29 \times 6}{29} }{ \frac{ - 140 + 29}{29} }$

$= \frac{ \frac{100 - 174}{29} }{ \frac{ - 111}{29} }$

$= \frac{ \frac{ - 74}{29} }{ \frac{ - 111}{29} }$

$= \frac{ - 74}{29} \times \frac{29}{ - 111}$

$= \frac{74}{111}$

[ each numerator & denominator is divided by 37 ]

$= \frac{2}{3} = r.h.s$

Hence

$x = \frac{ - 20}{29} is \: the \: solution$

Step-by-step explanation:

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