-8(3a-5)=56a

Question

I don't understand it

 

Answer 1

I'm going to provide this answer just in case you need more basic understanding of the equation.

So you said you were confused about this series of symbols:

-8(3a - 5) = 56a

because there is an equals sign in the middle, we call this series of symbols an equation, which means that the symbols to the left of the equals sign has the same value as the symbols to the right of the equals sign.

In other words whatever:

-8(3a - 5) is equal to.

56a is equal to the same thing.

Part of the problem clearly is what the hell does 56a equal? What does that mean?

In this case, 'a' is supposed to represent some number and we call 'a' a variable because the value of 'a' could vary, or change depending on the equation. 'a' could sometimes be 5 if we say a = 5, or in this case as Ayako figured out:

a = 1/2

We can double check this by replacing the symbol 'a' with the value we found. Let's do that just to make sure we got the right answer:

-8(3a - 5) = 56a

now turns into:

-8(3 * (1/2) - 5) = 56 * 1/2

Notice I replaced both instances of 'a' with 1/2, because for this equation that's what we found 'a' to equal.

So, rewriting so that we can do a little arithmetic:

(-8) * (3 * (1/2) - 5) = 56 * 1/2

(-8) * (3/2 - 5) = 28

(-8) * (3/2 - 5/1) = 28

(-8) * (3/2 - 10/2) = 28

(-8) * (-7/2) = 28

8 * 7 / 2 = 28

56 / 2 = 28

28 = 28

We have ended up with 28 equals 28, and that's true! Which means that the answer we found for 'a' must be the value we wanted!

Let me know if that answers your question about understanding it. Were there any other parts of the equation that were confusing?

Answer 2

So in this equation, it seems like you need to solve for a. 

The first step is to use the distributive property on the left side of the equation. 

The distributive property says the following: a(b + c) = a x b + a x c

So when you use this property on your equation, it will get you:

-8(3a - 5) = (-8) x 3a + (-8) x (-5) = -24a + 40. 

*Be careful about the minus signs (-) and remember that a (-) number multiplied by a (-) number is equal to a (+) number. 

So the left side of the equation is equal to -24a + 40. 

Now you have:

-24a + 40 = 56a.

The next step would be to either add 24a to both sides or subtract 56a from both sides. The reason why we do this is to put all the numbers with "a" in them on the same side of the equation. 

Adding 24a:

-24a + 40 (+24a) = 56a (+24a)

the -24a and +24a on the left side of the equation will cancel, and you get:

0 + 40 = 56a + 24a.

Then you simplify the right hand side of the equation. 

40 = 80a. 

Now to solve for a, all you have to do is divide both sides by 80.

40 = 80a

40/80 = 80a/80 (here, the 80s on the right hand side cancel, because when you divide a number by that same number, it becomes 1.)

40/80 = 1a

Now all you need to do is simplify the left hand side. 

40/80 = 1/2 = 0.5 = 1a.

 

You're done!