solve the following equation and verify your answer.
[tex] \frac{x {}^{2} - (x + 2)(x + 3) }{7x +1 } \: = \: \frac{2}{3} [/tex]
chapter- linear equation in one variable
class 8
go to h e l l mr K I T
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solve the following equation and verify your answer.
[tex] \frac{x {}^{2} - (x + 2)(x + 3) }{7x +1 } \: = \: \frac{2}{3} [/tex]
chapter- linear equation in one variable
class 8
go to h e l l mr K I T
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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
Verified answer
Answer:
[tex]\huge\mathfrak\purple{Solution} \: [/tex]
[tex] \frac{ {x}^{2} - (x + 2)(x + 3) }{7x + 1} = \frac{2}{3} \\ [/tex]
[tex]\frac{ {x}^{2} - [ (x + 2)(x + 3)] }{7x + 1} = \frac{2}{3} \\ [/tex]
[tex] \frac{ {x}^{2} - [ \: {x}^{2} + 3x + 2x + 6 \:] }{7x + 1} = \frac{2}{3} \\ [/tex]
[tex] \frac{ {x}^{2} - \: [ {x}^{2} + 5x + 6 ]}{7x + 1} = \frac{2}{3} \\ [/tex]
[tex] \frac{ {x}^{2} - {x}^{2} - 5x - 6 }{7x + 1} = \frac{2}{3} \\ [/tex]
[tex] \frac{ - 5x - - 6}{7x + 1} = \frac{2}{3} = \frac{2}{3} \\ [/tex]
By cross Multiplication
3(-5x - 6) = 2(7x + 1)
-15x - 18 = 14x + 2
-15x -14x = 18 + 2
-29x = 20
[tex]x = \frac{ - 20}{29} \\ [/tex]
[tex]verification \: for \: x \: = \frac{ - 20}{29} \\ [/tex]
[tex]l.h.s = \frac{ - 5x - 6}{7x + 1} \\ [/tex]
[tex] = \frac{ - 5( \frac{ - 20}{29} ) - \frac{6}{1} }{7( \frac{ - 20}{29}) + \frac{1}{1} } \\ [/tex]
[tex] = \frac{ \frac{100}{29} - \frac{6}{1} }{ \frac{ - 140}{29} + \frac{1}{1} } \\ [/tex]
[tex]l.h.s = \frac{ \frac{100 - 29 \times 6}{29} }{ \frac{ - 140 + 29}{29} } \\ [/tex]
[tex] = \frac{ \frac{100 - 174}{29} }{ \frac{ - 111}{29} } \\ [/tex]
[tex] = \frac{ \frac{ - 74}{29} }{ \frac{ - 111}{29} } \\ [/tex]
[tex] = \frac{ - 74}{29} \times \frac{29}{ - 111} \\ [/tex]
[tex] = \frac{74}{111} \\ [/tex]
[ each numerator & denominator is divided by 37 ]
[tex] = \frac{2}{3} = r.h.s \\ [/tex]
Hence
[tex]x = \frac{ - 20}{29} is \: the \: solution \\ [/tex]
Step-by-step explanation:
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