Solve the following equation and check your answer:

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

We have:

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

⇒ 18x + 12 - 30x + 5 = 3x - 24 - 35x + 30 + 9x $\quad$[Removing brackets]

⇒ -12x + 17 = -23x + 6

⇒ -12x + 23x = 6 - 17 $\quad$[Transposing +17 to RHS and -23x to LHS]

⇒ 11x = -11

⇒ x = $\dfrac{-11}{11}$

⇒ x = $\dfrac{-1}{1}$

∴ x = -1

Check:

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

= 6(-1) - 5(-7)

= -6 + 35

= 29

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

= 3(-9) - 5(-13) - 9

= -27 + 65 - 9

= 29

Hence, LHS = RHS.