Question

8(4-a)=2a

Answer :16/5 or 3.2

I need help with the checking the answer not the equation. We check a solution to an equation by replacing the variable in the equation with the value of the solution. A solution should result in a true statement when simplified. This is what I need. Thank you.

Answer 1

We know that the problem we are going to be dealing with is an equation. The big question is, what should we do? What steps should be taken to get to the answer? There are several steps. One of them is expanding the equation. We can't solve until we expand the left side. So the way we're going to do it is: the distributive property. This one states that if you have an
`a` term multiplied by the sum of
`b` and
`c` (the last two terms are in parentheses), then, in a sense,
`a` gets "distributed" and what results is this:

`\darkblue{ab+ac}`. So now we apply that to our problem:
`8(4-a)=32-8a`. Now we make the replacement:
`32-8a=2a`. Then, notice that we have
`a` terms on both sides. What we do is we subtract
`2a` from the right and left and subtract
`32` from the left and add to the right:
`-8a-2a=-32`. Now let me share a little trick with you. First, we can add the
`a` terms together:
`-10a=-32`. Next, if you have minus signs on both sides, you clear them:
`10a=32`. Now divide both sides by 10. Here another trick comes into play: If you divide by 10 you move the decimal sign 1 place to the left.

`a=3.2`

Now for the checking - put
`3.2` for
`a` and simplify. The answer should be a statement true for all values of
`a`. Let's go.

`8(4-3.2)=2(3.2)`

`8(0.8)=6.4`

`6.4=6.4` is the result. Since the statement is true, we understand that the solution WAS correct and that
`3.2` IS the value of
`a` in the equation
`8(4-a)=2a`.

Answer 2

8(4-a)=2a

32-8a=2a

32=10a....dividing through by 10a we get..

32/10=10a/10

3.2=a

answer is 3.2