Algebra equation with brackets problem

Question

So I'm reading through an introductory Maths book. I'm solving equations with brackets as was described in the book. I solved all but the last 2 questions which the author didn't mention or explain a method to working out the answer. Here they are:

1. 8x - (3x -7) = 2(x + 3) + 1
2. 5(3x + 4) = 9 + (6x - 7)

So let's say for the first question, I know how to expand the second brackets 2(x + 3), but I have no clue how to expand the first one 8x - (3x -7). There's no number directly outside the brackets to multiply them by.

Any help will be much appreciated. Thanks :)

Answer 1

No number written means it is an implied 1.

Answer 2

Rethink 8x - (3x - 7) as 8x + –1(3x + –7).

Then apply distribution: 8x + (–1 * 3x) + (–1 * –7).

Answer 3

a - b is really just shorthand for a + -1*b.

Answer 4

8x - (3x - 7) is almost the same as it'd be without parentheses, you just have to remember the negative. So you might think of it as 8x + (-1)(3x - 7)

Answer 5

this is brackets = \[\]

this is parenthesis = ()