How to know when to change signs or put brackets in linear equations? I’m not sure when I should change signs in an equation or put brackets (which is one of the causes of sign changes). For example $2-3(q-1) = 10-(q-1)$ should I solve the left side like this: multiply 3 with $q$ and 3 with -1 and add a minus sign in front. Will this result in $2-3q-1$ or $2-(3q-1)$ which is $2-3q+1$? And why is that so? OR multiply -3 with q and -3 with 1 resulting in $2-3q+1$.
The correct answer is $2-3q+1$ on the left side. But I am not sure why.
 A: In case of multiplication, we have a multiplicand and a multiplier. Consider $3 \times 2$ as an example, 3 is multiplicand and 2 is the multiplier.
If both multiplicand and multiplier are of same sign then the result of multiplication will be positive. If multiplicand and multiplier are of opposite sign then result will be of negative sign.


*

*$3 \times 2 = 6$ both 3 and 2 have same sign (+ and +) there fore
result is also positive.

*$-3 \times 2 = -6$ 3 has - sign but 2 have + sign so, result will have - sign.

*Similarly, $3 \times (-2) = -6$ due to same reasons.

*$-3 \times (-2) =6 $, Since both have same sign, So result is also positive.


Now coming to your question. $2-3(q-1)=10-q+1$
In the left-hand side, leave 2 aside and concentrate on $-3 \times (q-1)$. 
A: These may help you
$a(b+c) = ab +ac$
$-a(b+c) = -ab -ac$
$a(b-c) = ab - ac$
$-a(b-c) = -ab -(-ac) = -ab +ac$
A: Try to multiply the bracket $(q-1)$ with $3$ first. You have to multiply each element in the bracket by $3$ so that you have $(3\cdot q - 3)$. Therefore the left hand side is $2 - (3q - 3)$. Now eliminate the bracket, that means changing the signs of every element in the bracket. Doing that you have $2 - 3q + 3$. I hope this one helps.
