I don't understand this formula…!

[TheSnooze]

Could someone please explain this answer to me? I can not wrap my head around how we get from the formula to the answer number 4 at the bottom:

That would be amazing! Thanks

[garypettie]

Hi @TheSnooze,
Here’s each stage of the process so you can reveal it one step at a time:

14a + 2(3b + 5) = 30
            14a = 30 - 2(3b + 5)  <- Subtract 2(3b + 5) 

Note: you could expand everything on the left and do the calculation with more stages, but there’s no real need to do that.

This is the point where I’d expand those parentheses and then simplify the RHS.

14a = 30 - 2(3b + 5) 
14a = 30 - 6b - 10    <- Expand the parentheses
14a = -6b + 20        <- Simplify

14a = -6b + 20
a = (-6b + 20) / 14   <- Divide both sides by 14
a = (-3b + 10) / 7    <- Simplify

That final stage of simplification may have tripped you up.
The trick is to notice that everything on the right side is divisible by 2, so this answer isn’t yet in its simplest form.
It’s just like how we might simplify 2/4 = 1/2. None of the proportions are changing, so we’re not really change the equation - We’re just made it easier to read.

I hope that helps explain things for you but, if you have any follow up questions, just let me know.

[TheSnooze]

Ah thanks… That was nagging my brain. Actually what tipped me up was the whole process of moving things from left to right. I know how to do that but for some reason my brain just locked up and I couldn’t crack it. To subtract the whole 2(3b + 5) hasn’t even crossed my mind! I simplified the parentheses first thing and that overcomplicated everything. Thanks for taking the time… Greetings!

[garypettie]

Yeah, that happens to the best of us! I’ve spent hours looking at equations trying to figure them out, only to realize I’d been missing something simple

Whenever you see things nicely wrapped in parentheses like that you can always treat it as a singular argument in the equation, so sometimes factorizing things first can make your life a lot easier (especially if you’re trying to tackle some unwieldly beast of an equation).

If you expand first you’d get:

14a + 2(3b + 5) = 30
14a + 6b + 10 = 30     <- Expand parentheses
14a + 6b = 30 - 10     <- Subtract 10 from both sides
14a + 6b = 20          <- Simplify
14a = -6b + 20         <- Subtract 6b from both sides
a = (-6b + 20) / 14    <- Divide both sides by 14
a = (-3b + 10) / 7     <- Simplify

So you can do it both ways.

[TheSnooze]

It looks so easy now. But when I tried on my own it completely overwhelmed my little artist’s brain.