Verified answer

[tex]\large\underline{\sf{Solution-}}[/tex]

Given equation is

[tex]\sf \: \dfrac{9x + 7}{2} - \bigg(x - \dfrac{x - 2}{7} \bigg) = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{9x + 7}{2} - \bigg( \dfrac{7x - (x - 2)}{7} \bigg) = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{9x + 7}{2} - \bigg( \dfrac{7x - x + 2}{7} \bigg) = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{9x + 7}{2} - \dfrac{6x + 2}{7} = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{7(9x + 7) - 2(6x + 2)}{14} = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{63x + 49 - 12x - 4}{14} = 36 \\ \\ [/tex]

[tex]\sf \: \dfrac{51x + 45}{14} = 36 \\ \\ [/tex]

[tex]\sf \: 51x + 45 = 36 \times 14 \\ \\ [/tex]

[tex]\sf \: 51x + 45 = 504 \\ \\ [/tex]

[tex]\sf \: 51x = 504 - 45 \\ \\ [/tex]

[tex]\sf \: 51x = 459 \\ \\ [/tex]

[tex]\sf \: x = \dfrac{459}{51} \\ \\ [/tex]

[tex]\bf\implies \:x = 9 \\ \\ [/tex]

Verification :-

Consider LHS

[tex]\sf \: \dfrac{9x + 7}{2} - \bigg(x - \dfrac{x - 2}{7} \bigg) \\ \\ [/tex]

Put x = 9, we get

[tex]\sf \: = \: \dfrac{9(9) + 7}{2} - \bigg(9 - \dfrac{9 - 2}{7} \bigg) \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{81 + 7}{2} - \bigg(9 - \dfrac{7}{7} \bigg) \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{88}{2} - \bigg(9 - 1 \bigg) \\ \\ [/tex]

[tex]\sf \: = \: 44 - 8 \\ \\ [/tex]

[tex]\sf \: = \: 36 \\ \\ [/tex]

[tex]\bf\implies \:LHS \: = \: RHS \\ \\ [/tex]

Hence, Verified

Answer:

x = 9

Step-by-step explanation:

Given equation

( 9x + 7 )/2 - [ x - ( x - 2 )/7 ] = 36

⇒( 9x + 7 ) /2 - x + ( x - 2 )/7 = 36

Taking LCM

⇒ [ 7( 9x + 7 ) - 14x + 2( x - 2 ) ] / 14 = 36

⇒ 63x + 49 - 14x + 2x - 4 = 36 × 14

⇒ 65x - 14x + 45 = 504

⇒ 51x = 504 - 45

⇒ 51x = 459

⇒ x = 459/51

⇒ x = 9

Let's check the answer

Substitute the value of x in the equation

⇒ ( 9x + 7 )/2 - [ x - ( x - 2 )/7 ] = 36

⇒ [ 9(9) + 7 ]/2 - [ 9 - ( 9 - 2 )/7 ] = 36

⇒ ( 81 + 7 )/2 - ( 9 - 7/7 ) = 36

⇒ 88/2 - ( 9 - 1 ) = 36

⇒ 44 - 8 = 36

⇒ 36 = 36

LHS = RHS

Hence the answer is verified

Therefore the value of x is 9.