Rebulicans believe that that if you lower taxes the people will?

Yes that seems to be the case.

they were byzantines

8 - (2a + 7) = a + 40     distribute/multiply - into (2a + 7)

8 - 2a - 7 = a + 40

1 - 2a = a + 40       add 2a on both sides

1 = 3a + 40         subtract 40 on both sides

-39 = 3a       divide 3 on both sides

-13 = a

[proof]

8 - (2a + 7) = a + 40

8 - (2(-13) + 7) = -13 + 40

8 - (-26 + 7) = 27

8 - (-19) = 27

8 + 19 = 27

27 = 27