Question

6(3x+2) -5(6x-1) = 3(x-8) -5(7x-6)+9x

Answer 1

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Answer 2

Answer:

The value of x is - 1.

Step-by-step-explanation:

The given equation is

6 ( 3x + 2 ) - 5 ( 6x - 1 ) = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

We have to find the value of x.

Now,

6 ( 3x + 2 ) - 5 ( 6x - 1 ) = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

↣ ⇒ 6 * 3x + 6 * 2 - 5 * 6x - 5 * ( - 1 ) = 3 * x + 3 * ( - 8 ) - 5 * 7x - 5 * ( - 6 ) + 9x

⇒ 18x + 12 - 30x + 5 = 3x - 24 - 35x + 30 + 9x

⇒ 18x - 30x + 12 + 5 = 3x - 35x + 9x - 24 + 30

⇒ - 12x + 17 = - 32x + 9x + 6

⇒ - 12x + 17 = - 23x + 6

⇒ - 12x + 23x = 6 - 17

⇒ 11x = - 11

⇒ x = - 11 ÷ 11

⇒ x = - 1

∴ The value of x is - 1.

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Verification:

The given equation is

6 ( 3x + 2 ) - 5 ( 6x - 1 ) = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

We have, x = - 1.

By substituting x = - 1 in the LHS of the given equation, we get,

6 ( 3x + 2 ) - 5 ( 6x - 1 ) = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

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

⇒ LHS = 6 [ 3 * ( - 1 ) + 2 ] - 5 [ 6 * ( - 1 ) - 1 ]

⇒ LHS = 6 ( - 3 + 2 ) - 5 ( - 6 - 1 )

⇒ LHS = 6 ( - 1 ) - 5 ( - 7 )

⇒ LHS = - 6 + 35

⇒ LHS = 29

Now, by substituting x = - 1 in the RHS of the given equation, we get,

6 ( 3x + 2 ) - 5 ( 6x - 1 ) = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

RHS = 3 ( x - 8 ) - 5 ( 7x - 6 ) + 9x

⇒ RHS = 3 ( - 1 - 8 ) - 5 [ 7 * ( - 1 ) - 6 ] + 9 * ( - 1 )

⇒ RHS = 3 ( - 9 ) - 5 ( - 7 - 6 ) - 9

⇒ RHS = - 27 - 5 * ( - 13 ) - 9

⇒ RHS = - 27 + 65 - 9

⇒ RHS = 38 - 9

⇒ RHS = 29

∴ LHS = RHS

Hence verified!