Solve the following equation and check your answer:

7 - 2(5 - 3x) = 4(x - 3) + 5

We have:

7 - 2(5 - 3x) = 4(x - 3) + 5

⇒ 7 - 10 + 6x = 4x - 12 + 5 $\quad$[Removing brackets]

⇒ -3 + 6x = 4x - 7

⇒ 6x - 4x = -7 + 3 $\quad$[Transposing -3 to RHS and +4x to LHS]

⇒ 2x = -4

⇒ x = $\dfrac{-4}{2}$

⇒ x = $\dfrac{-2}{1}$

∴ x = -2

Check:

LHS = 7 - 2(5 - 3x)

= 7 - 2[5 - 3(-2)]

= 7 - 2(11)

= -15

RHS = 4(x - 3) + 5

= 4(-2 - 3) + 5

= -20 + 5

= -15

Hence, LHS = RHS.