Solve the following equation and check your answer:

p - (2p + 5) - 5(1 - 2p) = 2(3 + 4p) - 3(p - 4)

We have:

p - (2p + 5) - 5(1 - 2p) = 2(3 + 4p) - 3(p - 4)

⇒ p - 2p - 5 - 5 + 10p = 6 + 8p - 3p + 12 $\quad$[Removing brackets]

⇒ 9p - 10 = 5p + 18

⇒ 9p - 5p = 18 + 10 $\quad$[Transposing -10 to RHS and +5p to LHS]

⇒ 4p = 28

⇒ p = $\dfrac{28}{4}$

⇒ p = $\dfrac{7}{1}$

∴ p = 7

Check:

LHS = p - (2p + 5) - 5(1 - 2p)

= 7 - 19 - 5(-13)

= -12 + 65

= 53

RHS = 2(3 + 4p) - 3(p - 4)

= 2(31) - 3(3)

= 62 - 9

= 53

Hence, LHS = RHS.