Question

x – 2x + 2 – 16/3x + 5 = 3 – 7/2x

Answer 1

Answer:

x = 24/17

Step-by-step explanation:

Solution↴

x – 2x + 2 – 16/3x + 5 = 3 – 7/2x

➪ Let us rearrange the equation

x – 2x – 16x/3 + 7x/2 = 3 – 2 – 5

By taking LCM for 2 and 3 which is 6

(6x – 12x – 32x + 21x)/6 = -4

-17x/6 = -4

By cross-multiplying

-17x = -4×6

-17x = -24

x = -24/-17

x = 24/17

Let us verify the given equation now,

x – 2x + 2 – 16/3x + 5 = 3 – 7/2x

By substituting the value of ‘x’ we get,

24/17 – 2(24/17) + 2 – (16/3)(24/17) + 5 = 3 – (7/2)(24/17)

24/17 – 48/17 + 2 – 384/51 + 5 = 3 – 168/34

By taking 51 and 17 as the LCM we get,

(72 – 144 + 102 – 384 + 255)/51 = (102 – 168)/34

-99/51 = -66/34

-33/17 = -33/17

Hence, the given equation is verified

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Answer 2

Step-by-step explanation:

$\blue{ \bf{ \underline{Question \: : - }}}$

${ \bf{x - 2x + 2 - \frac{16}{3x} + 5 = 3 - \frac{7}{2x}}}$

$\star{ \pink{ \underline{ \underline{ｓｏｌｕｔｉｏｎ : - }}}}$

$\implies{ \bf{x - 2x - \frac{16}{3x} + \frac{7}{2x} = 3 - 5 - 2}}$

$\implies{ \bf{ \frac{ {6x}^{3} - {12x}^{3} - 16x + 7x }{ {6x}^{2} } = - 4}}$

$\implies{ \bf{ - {6x}^{3} - 9x = - {24x}^{2}}}$

$\implies{ \bf{ { - 6x}^{3} + {24x}^{2} - 9x = 0}}$

${\implies{ \bf{ { 6x}^{3} - {24x}^{2} + 9x = 0{\: \: \:( Dividing \: as( - 1)}}}}$

$\implies{ \bf{ 3x( {2x}^{2} - 8x + 3) = 0}}$

=> 2x²-8x+3 =0

=> 2x²-2x -3x + 3 =0

=> 2x ( x-1) -3(x-1) =0

=> (2x-3) (x-1) =0

________________________________

Hance,

2x -3 =0

=> 2x = 3

=> x = 3/2

ｏｒ.

ｘ-１=０

ｘ-１=０ => ｘ = １