Solve the following equation and check your answer:

2(3y - 2) - 4(2y - 5) = 9

We have:

2(3y - 2) - 4(2y - 5) = 9

⇒ 6y - 4 - 8y + 20 = 9 $\quad$[Removing brackets]

⇒ -2y + 16 = 9

⇒ -2y = 9 - 16 $\quad$[Transposing +16 to RHS]

⇒ -2y = -7

⇒ y = $\dfrac{-7}{-2}$

∴ y = $3\dfrac{1}{2}$

Check:

LHS = 2(3y - 2) - 4(2y - 5)

= $2\left(3 × \dfrac{7}{2} - 2\right)$ - $4\left(2 × \dfrac{7}{2} - 5\right)$

= $2\left(\dfrac{17}{2}\right)$ - 4(2)

= 17 - 8

= 9

RHS = 9

Hence, LHS = RHS.