ok i need a refresh on linear equations again :/ I know I can do it when its without the extra numbers like this 2(4x-7)=3(7x+5)...but when its the extra numbers added to it like the +6 or 9-5(...) I get lost on which way to go after
9 - 5 (6z + 3) = (-7z - 7) + 6
Then 9 - 30z + 15 = -7z - 7 + 6
right?
So after, do I subtract 15 from the 9 or subtract 9 from the 15 and add 7 to the 6 or subtract 6 from the 7 (is that a 7 or -7?)...I get lost with the signs a bit too... Bare with me, I just seem to be missing a step or going wrong way.
Whether you use BIDMAS or PEMDAS, brackets/parenthesis come first.
It is important to remember in the above case that you are multiplying the bracket on the left hand side (hereby thereafter abbreviated as LHS) by MINUS five, not POSITIVE five. The number multiplying the bracket must multiply the
whole bracket, and that number is negative 5. -5 is a different number than 5!
LHS therefore becomes
9 - 5(6z+3)
=> 9 - 30z - 15
Your Right Hand Side (RHS) is correct.
=> 9 - 30z - 15 = -7z - 7 + 6
[-7 + 6 = -1; 9 - 15 = -6]
=> -30z - 6 = -7z - 1
Now, you want to take all z terms to one side and constants to another. You can do this to either side.
Adding 30z (or you can think of it as subtracting -30z, and two negatives make a positive);
=> -6 = 23z - 1
Adding 1 (or you can think of it as subtracting -1, and two negatives make a positive);
=> -5 = 23z
Now, divide both sides by 23 to get a singular z (23/23 = 1);
-5/23 = (23/23)z
-5/23 = z
Just take your time when negatives are involved and double check all calculations you make, especially with those brackets!
