Question

How do you solve `4.7(2f - 0.5) = -6(1.6f - 8.3f)`?

Answer 1

`f = -47/(616)`

Explanation:

We first start out by using the distributive property; that's `a(b+c) = ab+ac`. Let me demonstrate:

`4.7(2f-0.5) = -6(1.6f-8.3f)` (original problem)
`(4.7*2f-4.7*0.5) = -6(1.6f-8.3f)` (distributing the 4.7)
`9.4f-2.35 = -6(1.6f-8.3f)` (simplifying)

Now to combining like terms and a little multiplying:

`9.4f-2.35 = -6(-6.7f)` (combining the `1.6f` and `-8.3f`)
`9.4f-2.35 = 40.2f` (multiplying the `-6` and `-6.7f`)

Now we proceed to solving this 2-step equation:

`-2.35 = 30.8f` (subtracting `9.4f` from both sides)
Here, we encounter a problem: to finish, we need to divide by `30.8`; that way, we solve for `f`. But in doing so, we get a repeating decimal. This would be nice for an approximate answer, but we want something definite. So, we convert our decimal numbers to whole numbers by multiplying by 100. Watch:

`-2.35*100 = 30.8f*100`
`-235 = 3,080f`

It certainly isn't pretty, but it works. Finally, finally, we divide by `3,080` to get our result:

`f = -235/(3,080)`
`f = -47/(616)` (simplifying the fraction)

Hey, it's a weird answer, but the math never lies. Our result is `f = -47/(616)`.

Answer 2

First collect like terms inside the brackets;
#4.7(2f-0.5)=-6(-6.7f)

Then, you would want to multiply into the brackets;
`9.4f-2.35=40.2f`

Collect like terms on either side of the equals sign;

`-2.35=30.8f`

Divide both sides by 30.8;

`-2.35/30.8=(30.8f)/30.8`

Finally, compute the result;

`f=-47/616`

Hope that helps :)